Question
A pet store has 30 animals. Some are cats and the rest are dogs. The cats cost $50 each. The dogs cost $100each. If the total cost for all 30 animals is $1900, how many cats are there?
Hint:
let the no. of cats be x and let the no. of dogs be y
Given total no. of animals = no. of cats + no. of dogs = 30
Given total cost of all animals = cost of x cats + cost of y dogs = $1900.
The correct answer is: 22 cats
Ans :-The animal shop has 22 cats .
Explanation :-
Step 1:- construct the system of linear equations
let the no. of cats be x and let the no. of dogs be y
Given total no. of animals = no. of cats + no. of dogs = 30
So, x + y = 30 — eq1
Given total cost of all animals = cost of x cats + cost of y dogs = $1900.
cost of x cats = x
cost of each cat ( The cats cost $50 each)
cost of x cats = 50x (in $ )
cost of y dogs = y
cost of each dog ( The dogs cost $100each)
cost of y dogs = 100y (in $)
So total cost of all animals = 50x + 100y = 1.900 — eq2
Step 2 :- eliminate x to find value of y
Doing eq2 - 150
eq1 to eliminate x
We get 50x + 100y - 50(x + y) = 1,900 - 50(30)
![not stretchy rightwards double arrow 100 y minus 50 y equals 1 comma 900 minus 1 comma 500](data:image/png;base64,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)
![not stretchy rightwards double arrow 50 y equals 400 not stretchy rightwards double arrow y equals 8](data:image/png;base64,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)
∴ y = 8
Step 3:- substitute the value of y in eq1 to get the value of x
![x plus y equals 30 not stretchy rightwards double arrow x plus 8 equals 30](data:image/png;base64,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)
![not stretchy rightwards double arrow x equals 30 minus 8](data:image/png;base64,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)
∴ x = 22
∴ The animals shop has 22 cats and 8 dogs in total of 30 animals.
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If the radius and height of a cylinder are in ratio 5 :7 and its volume is 550 cubic.cm, then find the radius?
If the radius and height of a cylinder are in ratio 5 :7 and its volume is 550 cubic.cm, then find the radius?
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)
Which of the following is true about the standard deviations of the two data sets in the table above?
Note:
We could also calculate the standard deviation for both the data sets
The formula for standard deviation is
Where, = standard deviation
= total number of terms
= terms given in the data
= mean
After finding both the standard deviations, we can compare them. This is a tedious task and needs precision.
![](data:image/png;base64,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)
Which of the following is true about the standard deviations of the two data sets in the table above?
Note:
We could also calculate the standard deviation for both the data sets
The formula for standard deviation is
Where, = standard deviation
= total number of terms
= terms given in the data
= mean
After finding both the standard deviations, we can compare them. This is a tedious task and needs precision.
50 animals are there in a shed. Some of the animals have 2 legs and the rest of them have 4 legs. In total there are 172 legs. Frame the system of linear equations and use elimination method to solve .
50 animals are there in a shed. Some of the animals have 2 legs and the rest of them have 4 legs. In total there are 172 legs. Frame the system of linear equations and use elimination method to solve .
The area of trapezium is 384 sq.cm. If its parallel sides are in the ratio 3:5 and the perpendicular distance between them 12cm. The smaller of the parallel side is
The area of trapezium is 384 sq.cm. If its parallel sides are in the ratio 3:5 and the perpendicular distance between them 12cm. The smaller of the parallel side is
A Rectangular sheet of paper 44 cm x 18 cm is rolled along its length and a cylinder is formed. What is the volume of the cylinder so formed?
A Rectangular sheet of paper 44 cm x 18 cm is rolled along its length and a cylinder is formed. What is the volume of the cylinder so formed?
The difference between two parallel sides of a trapezium is 8cm. The perpendicular distance between them is 19cm while the area of trapezium is 760 sq.cm. What will be the lengths of the parallel sides.
The difference between two parallel sides of a trapezium is 8cm. The perpendicular distance between them is 19cm while the area of trapezium is 760 sq.cm. What will be the lengths of the parallel sides.
A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?
A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients?
The sum of 3 consecutive natural numbers is 75. Find the numbers.
The sum of 3 consecutive natural numbers is 75. Find the numbers.
Find three consecutive even numbers whose sum is 312.
Find three consecutive even numbers whose sum is 312.
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)
Triangles ABC and DEF above are similar. How much longer than segment EF is segment DE ?
Note:
There are three ways to prove that two triangles are similar- AAA,
SAS, SSS.
AAA means that the corresponding angles are equal,
SAS means two sides of the triangles are in equal ratio and the angles between these two sides are equal,
SSS means that all three corresponding sides have equal ratio
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6UFGN1mqgaGnJN904R3ktK2kslJCRgjjTj7+dPZLSZho0aaR3JramKQn76Mbb+uJmDJ1IosPpz+wND+Wev1vgDivMCpw/tYevWXZRUbs0Tw/sio/7iasgUPC+0d+9epkychMEAMfHxNGnSROtIbs9pK+TIL9s4XRJE6/atqFx8iNlx0/klxQqAoljJPJvMzg2rWL/tCA6N8wr3IUfSXubI4cPEmM2UlJQwbcZ0WrZqqXUkD6CiolC18W08M6Q9lYG7bqnGvn/FkXD4LHc2bIaPXyhd7htM+v4tLE83IJcHiaslJe1FjiYeJSoikrzcPKLjYmjXvr3WkTyEAb/A6rTtWP3Sv504DCZCqteiTq3Q37/LYbfhdClyib24JlLSXiLpZBJTY2M5m5JCdHwcHTt20jqSx1KsRRz5eTeV2/bkzraXm3UjxNWRMWkvcPr0aabGxXH8+HEmRUTQtWtXrSN5MCdnj+xiyyl4ZMQwwuWqenGDpKQ9XGpqKrOmzyAhIYGx48fT+y5ZOLY85aUeZ/f+M9w8YDg9m1fB6XSg/L6spAGD4dJ/WoYUbkVK2oOdy8hgzsxZ7NyxnbHjxnJ/v75aR/JYqqqQnZzA6hVfU1C1Lbc1CyTpaAI/7zzABefF7zGaFBw2Ozab46pWxRECZEzaY2VlZTH3/Q/YtHEjo8e8xYCBA7WO5NFsBWms/+wjPtuSyW09fPjwwHryss6j3nQPXbp3BMVCWtIhkrMKsRaf5/DxTDo3qUWg/AWKK5CXiAfKzc1l/rx5rF2zhpdfHcUjjz2mdSQPp6A6LPjUaEG/fq0wKk4cAb7Uq1aP9nd1oxLgcFjITs8jvNN9PGQIJO9UEsUNpKTFlclLxMMUFBSwaMFCvvziC/794os89fRwrSN5ASOBYc159Pnml/0OX/9QOt8/iL/exVuI/03GpD1IcVERnyxezKdLl/LU8OE8/8ILWkcSQtwgKWkPUVpSwrJPP2PhRwsY+tijvDzqFa0jCSHKgJS0B7BYLHyxfDnz5s5l0KDBvP7GGxhkXUIhPIKUtJuzWq18/dXXzJk9h/v79WP02DH4+MipBiE8hZS0G7Pb7axetYoZ06bRq3dvxo4fh5+f35V/UAjhNqSk3ZTD4WD9uu+YHj+VLrd3YcLECQQFBWkdSwhRxqSk3ZCiKGzauJG4mIt3sps4eTLBsnCsEB5JStrNKIrCz5s3ExsdTdNm/2ByZAShoaFX/kEhhFuSknYz27ZuwxwRSZ064UyJjKJWrVpaRxJClCMpaTeya9cuoqOiqFK1KlHR0dSrV1frSEKIciYl7Sb2JiRgjojAZDISYY6i8U2NtY4khKgAMqHWDRw+dAhzZCR2u4PY+DiaN7/8PSKEEJ5FSlrnjiYeJToqirzcPGKnxtOmbVutIwkhKpCUtI6dPHGCaLOZ9PR0omNj6dCxo9aRhBAVTEpap5KTk5kaF8/J48eJionmti5dtI4khNCAnDjUobMpKUyNi+PggQNMjoigZ69eWkcSQmhESlpn0tPSmD1zJrt2/MKYcWO5u889WkcSQqdU1Ct/k9uT4Q4dOXfuHLNnzmLz5p95+51x9H/wQa0jCaEbquKiMDuNs+k5OFQDfv5+mFCx2x0YA6vTokVD/DzwDr1S0jqRnZXF/Llz2bB+Pa+NfpNBgwdrHUkInVEozU3l+6Xz+TE9mEeH9qW6r43UE4c4lFeDdyb+h5q+Wmcse1LSOpCbm8uH8+ez+ptVjHzlFYYNG6Z1JCF0x2D0pVbDloQHlJBjaMY9/fpR02Qjq2lNLvyYgqeOfUhJa6ygoIAlixax4vPljHjuOYaPkIVjhbgcu91Kdp6Tm2/vTJg/gC+BNZowaFALqnhom3no03IPxcXFLF2yhKWfLOXJp5/mPyNf0jqSEDqmYLekceR0CcE3O0hLSSLnfAqncyrzYL/bPHYWhKc+L90rLS3li8+Xs/CjhTw0cCAvvzIKg8EDz3oIUVZUB9bzyaQVO1HyM9m5/WdWfbaU3WkOjy4yOZLWgNVqZcUXK/jg/ffp/2B/3nxrNEaTSetYQuiaaneSdfI0ztCG9Ht4CLcG5VLL10hBk2ZaRytXUtIVzGazsXrVat6fPYdevXox+u0x+Pv7ax1LCN1zOG0kn0kloHoz2jYJpirBdO8/lGKHi8KiUqqEVNI6Yrnw5E8JuuN0Ovh27Vqmx8fTrXs33pF1CYW4aqotj+Mnk/EPa0rN376m2jm+60f2nMjRNFt5kiPpCuJyOtm0cSNT4+Jp274d70ycQIisSyjElakq9pIcjuzeycFTWTjb53P85EmclmLOnzrADztO02/kvVqnLDdS0hVAVVV++P57zJFmWrVqRURUFNWqVdM6lhBuQsFalMPZHCsd+z6GbyUfEvbux1exkpdTQuse/ejUIEDrkOVGSrqcqarK1i1biDFHU69+fSZHRhAWFqZ1LCHch8FESN2WDPhXS62TaELGpMvZtm3biJw8hbCwMKJjoqlTp47WkYRwS7k5uZw5fRpV9dBLCy9DSrocJezZQ3SUmcDAQCLNZho0bKh1JCHcUkZGBrNnziTGHI3VatU6ToWS4Y5ykrAngSkTJ2M0GoiOi+Wmpk20jiSEW8rMzOSD997jo/nzqV27DjarlcDAQK1jVRgp6XJw+NAhYs3RXLhQSvyM6bRo6Z1jaULcqJycHD6aP581q9bQqVNnikuKMRq9awDAu55tBTiamEh0pJnc3BwiY8y0a9dO60hCuKX8/HwWfvQRX3/5Nc+/+CJDhg7lQukFrWNVOCnpMpR0MompcXGknD3LpIgpdOrUWetIQriloqIilixazGdLP+Wp4U/x3AvPYTAacLlc4GW3uJGSLiOnT59mWlw8x48dZ+LkiXTt1k3rSEK4pZKSEj795BMWf/wxjw8bxksvv4zL6cLhcFy8CZl3Te6Qki4LqampzJo+g4SEPYx9Zzx33X231pGEcEsXLlzgi8+X8+HceQwcPIhX33gdAEVRvO0A+ndS0jcoIyODObNmsX37dsaMfZv7+/bVOpIQbslqtbJyxUren/MeD/Tvz+gxYzDJ3SGlpG9EVmYmc997n00bN/Ha66/z0KBBWkcSwi3ZbXbWrFrF7Bkzueueu3j7nfH4+flpHUsXpKSvU05ODh/Om8+3a9cyctTLPPLYo1pHEsItOZ1Ovl27lmnxU+na7Q7Gv/sugQGeey+OayUlfR0K8vP5+KMFrFzxBc+98DxPD5d1CYW4Hk6nk+83biQ+Lpabb72ViZMnExwcrHUsXZGSvkZFRUUsWbyYZZ9+ylPDh/Pv55/XOpIQbklRFH768UeizdE0a96cSVMmU1XuDvkXUtLXoKSkhM+WLuXjhR/z2OOP8/Irr2gdSQi3pKoq27dtI8Zspl79ekRGRcndIS9DSvoqXZwa9DkfzpvPwEEDefWN12XhWCGu0y87dxIVEUnVqtWIjIoivG5drSPplpT0VbBarXz15Ze8P+c9+j3wgEwNEuIG7E1IwBwRSUCAP+aYaBo2aqR1JF2TGyxdgd1uZ/WlqUE9e/dizLixsnCsENfpwP4DREVEYLfbmRo7nX808+yVvsuClPT/4HA4WL9uHdOnTqPLHXfw7sSJsnCsENcp8cgRoiMjKS4qJjo+jtZt2mgdyS1ISV+Gy+Xi+02biI+Lo02btrw7SRaOFeJ6nTh+nJjoaNIzMoiNj+OWW27ROpLbkDHpv6EoCpt/2kysOZqmTf9BRFQE1UOrax1LCLd06tQpYqNjOJ18mkizmS633651JLciR9J/4+LUoChq1a7FpIgIatWurXUkIdxSypkzTJ86jYMHDxJhjqJ7j+5aR3I7ciT9X3b98gvmiEiqVKmKOSaG+vXraR1JCLeUlprK9KnT2LN7NxMnTaRPnz5aR3JLUtJ/8NvUIKPJSERUJI1vuknrSEK4pXMZGbw3Zw5bfv6ZN98aTd8HHtA6ktuS4Y5LDh44QOSUCBxOBzHx8TRv0ULrSEK4pazMLN5/7z2+37iR0WPeYtDgwVpHcmtS0kBiYiIxUWby83KJmzaNNjI1SIjrkpuby0cffsia1Wt4edTLPPLYY1pHcnteP9xx4vhxoiOjOHfuPObYWDp07Kh1JCHcUkF+Ph8vWMCXK1bwwosvMPyZZ7SO5BG8+kj61KlTTI2PJykpCXNMNLd16aJ1JCHcUnFREZ9+spRPly5l2BNP8O8XXtA6ksfw2iPplDNnmBYbx+FDh5kUGcGdPXtqHUkIt1RaWsqyTz/j44ULeeTRRxkld4csU15Z0mmpqcyeOYtff/2VMWPf5h5ZOFaI62KxWPhq5UrmzZ1L3379eO2NNzD5ePUH9DLndSV9LiOD2bNmsXXLFt4eN45/9u+vdSQh3JLdbuebr75i9qxZ3Hvf/YwZNxZfX1+tY3kcryrprKws5s+bx6YNGxn5yigGDpaFY8W1MRgMGJD7iDscDtZ9+y0zp8/g9ju6Mnb8uHK9+ZjBYMBg8Kq6+p3XfC7Jzc3lw3nzWbNqNS+NepnHhw3TOpLQMafTiaoof/qawWjE4XTicrnAixd8cLlcbPhuPXHRMXTs1ImJkyZRObhyme3b5XL96W3QYDDgdDhwupyXvlAmD+U2vKKkCwoKWLJoEStXfMGIZ55l+IgRWkcSOuV0Ojl54gQnTyYRFBiIqqq/bzMYDdjtdtLT0zCZvPOo7rd1CWNjYmjeogWTpkyiWuiNr0uoKAppqWns37+foKBAVOUPv3eDAUVVOHH8xMXFNtT/sSMP5PElXVxczNLFS1i65BOeePJJXhr5ktaRhI5ZrVbWfbuOgvx8mrdsicvp/H2bwWDAarNRWnrh4tJpqpe1BbD5p5+InBJB48aNiYw2U71GzTLZr91uZ+eOHWzbupXbu96Bw+74/40GAy6nk+KiIlRVRfGyX7tHl3RpaSlffL6chQsWMGjw4IsLx3rxx1RxZaqqEhAYwL8eeJwWLVv+ZbvL5SLz/Hn27dvrVQd0KrBr505ioqKoWaMGEeYo6tSpU3b7V1WMRiP39+tL3379/vZ7AgID2bFtm7eNdnjuiUOr1crKL1bwwXvv0f/BB3lzzGhZl1BcFaPBgMVi+dttlgsWnA6H1xXFrp07mTxxEpWDQ4iOi6V+/fpl/hhGowGH3f6322w2Gzar1SsXf/bIkrbZbKz6ZhVzZs2i99138dbYt/Hzk3UJhbge+/fvJzrKjMFgIDI6mpuaNNEmiBcWNHjgcIfT6WTtmjVMj4une48evDNhAoGBgVrHEsItHThwgMjJU7DZbMTEx9GiRXOtI3kdjyppp9PJpo0bmT51Krd27MCESZMIDg7WOpZwIxfnQXP5j9UXN1ZkJM0cO3aUqbFx5OXlETd1Ku3atSu3x7o4D9pw2d/tb/9fvJH7lbTq4IJFISjoz8MXTqfz4sKxMbG0aduWqNgYqlSpolFI4a5MRiMGo/GyJW0ymVBV9TInDVVKC3PJLyzFqYB/UGWqhYYS4ONe9aKqKklJScyYOo1zGRmYY2K4tcOt5fqYJqMRDAaMxsv/3g0Gw6XfvTedsnWzklZddtKObGPX2coMeKDz7+EVRWFfwl7GjRlLVlYmfR/ox5afNlNSWuK1777i2hkMBmw2O7/u2kV+Xh4nT5zA4XD8abvdbufQgQMYTcY/vbYseWkkHk0ip7AUh8OJ3WahqLAQ39rtGfTPLgRU/NP5E8VhI+d8OkVWFwAmH198fHzw9Q+kamh1Av7QBNnZ2cREmfnmq68YOHgQmefPsfyzZSiqcpm93xiDwYDT6SQhIQEfkwmnw4nVYv39ohWDwYCiKOzYvv1P9ayqCqUFOWTnFeJSDZiMJgwGFZdLwRhQhQb1auIJUwXcqqQteams/ug9vnf04O4HOlP10tcdDgdJp07h7+9Pq9at2bRhI2tXr/HKM8HixhlNRs6cPsOGDRv/8iavqCq+vj707NUb30snowvTDrP6ixUcL63CbV17cGuHxvg7C9i1/nMWrVhFt7u60LD8rkS7opQAAAjmSURBVJi+KoqjlFP7N/H5Vzsx1W9L1w7N8HFaKSwowFitMXf27Eb90ItvJYUFBaSmpdHu5ptJS0tnxrTpKKpa7gc8RqMRFdizZ89fLr1XUTEajHTt3h0/P79LT0qhKOMEa5ctIyGnCvf2uYMQk42slJOcstblzTeGUcUDpka4TUkrLhsph3ZxKrMUa0A2OVaoeunwxM/Pj3vv60Pbdm0BFUUp/xeU8FwXP1ZfLIb/fh2pXPxoHhZWC5PJiL3gLGsWzmbFsWAmxI2hQ93fTlJXp8+QYVgq7yVQB5/OfYKCadi0FmmHE6l388P07HUH1pxzJO7+mS+Xv8e+5HzeeWUIVX2gfoMGzJw96+Kl8aqKWgEFDf9/HuDv3hDUS9urVav2+z1CDCYfqtdpRFDJaQ5mdWDinT0JNVwgPdRIyrYcnC48Yv6am5S0Qkn2GfYeL6TXwH6c+XwfGedVmja6+L/SYDAQGlqd0NDqGucUXsVlJXXvepZ+l0jfSZ/9oaAvMgXXoc/9dxOk9VgHgKri41TwqVmP27t2p3pIMIRUpe5NzaipZvBc/Ees730Xj9waSkBAAC3cZI1PxWjCZjdxS7euNKpeGahM5Vu78khtC5U9YawDN3mfcVmLOLFnF2qTrtzZozWBRbmczTyvdSzh5eyWYvb8vIXi4Bb06vbXizuMBl9CQirjo4OyUB0Osk4kUWIMpkHDP854UmjUoRN11EIOHTmhWb7ro2CzpJF46gJ1albiwoVistJTOHwsiwb/aIi/W7Tblen/SFp1kXv2AGs2HaTtwNYkHs7A4CzgTEY2UHaXpXoPJ9lnk0nLLsY/JIzGTeoT+PuLWaU0N4PUzEIMPgHUbtCIKgEe8kovB05nESmpmQRV60ltjcecr8TptJF8JhWfkAbc9F+321AAE+B0ld2JQVVxUZSVRlp2ERiNgIGgarVpHB5aZo+B6sSelcyZIift8jL4ZXsRZw7uJsnejHEdPGcxad2XtNOSx96t27CE1MGemsiRwhwCg1XOnD4HlN+8TU+kOC2kHt3N95u2cPRUKoX2QLoOGc6/+rTDV1UoPHeUb7/ZRElgTXwtWbhq3MLQgT0J1v2rRCsmfHx9UFxOXH+zVVWdOJ0GfH21P5R22IpJSU2jUv2u1P7jBpdC4ZkUcgyB3Neo7C71dliL2LZyAd8czKZygC+q0Y8WPR/h+QFlWNIOBzmnTmMNrkmLlk2p5JeLj8tGSKPmVCq7R9Gczv/8XGQl7eVgTk1GjnuO+gGgWvKoWrCP+cdP4UT3T0BHVGzFOezfcwD/xrcxuGMHflz+IfNiZtK64wI6BhWz8+tFrDkazszp/0JJXMPYCXPwb9SCYZ1rX3n3XsjXL4TmzRuz8ptEjqVD7bp/2Oi6wIlDBzHVvpmmtbUuaRVHSR6pqTnU7d/qT1scxVn8+MMOglp2pWeHsippFbsth+SUYlp370nDICMu1ZcGLRuU0f4vcjjsJCenEhzejvv6dCAM6HRza05bql7xZ92Jbj/LKg4LKUf2sHLpVxia3kb9Sydf7HYLir8fOQd2sS+jGKV8pm56HlXFaAqiTa+BPP7QPXTpcT9PPPkoNQoSOXbegq0knR827KVJt16E+ULVmzrTsXYxq7/drnVy3fINCKHjPf1pH1bC6s++5Oy5HIqKi8nLSmX3D6tZtWEvDj9dnDXEkpdOyjmVFm0b/f7V0pyz7Ny0ih0pfjz+72dpVmYX57pQrIWotW/mX48N5cGHBjN48AA6Nw8r08tQFFcJp85kEFK3JWGXvmasUpcmtT3pOFq3B6IKzuIsDv66lUPpLrqGGrEqEGBwYSnIItdaiSa1CknYm0jzuzsTEiAT7q7IYMQ/pDpNQi7922WntLiUgPBmNK/liyXnGMcyTfQPv3gDd5PBl9p1q5N68ChFQMhld+zFjD6EtbmHV18u4pPVv7Juk4Fm9athzUtn/+4D1Oo1nJZl+On+eqiqQlHmKX7Z9hNJmS66ZBwhuUrYxeGPxP0kHMnn7mdG82i3hmX3oIqCq7CI/AtZ7Fr7JZnncwlt3JZuXTtRs1JZVI6Ky1LA0YTt7Ek8g7OLnZyCUqpXreSRU291WtIGjAFVaNv9n7S8czD+/kG/TZTEv0pd7nlkJPcP88Gl+unizLk7shZm8Ouu/TTp8ygdqxvJPp5PidFEwG8LiRoNmPz9UUuLKFUhxBNf/WXAYDDRrMfDjG1zByeS0ym1OQiq25wB7Xvyj6b1tI6HqjjIz0znfHFl7nqoF67kQ+xzhuNncGEKbsyQ5wfRtHZZ39/GhG+lWrRpUouiwgIyk/ez6pvVHM4YzdtP9bjx0lFVHMV5nEnJpmGHu6kUZiExNZduUtIVyYBPUFUaNf3vsSUjgVXDaFI17G9/Slwd1V7I4Z0/kay24N/D78OIA9XPHz/Fhf23deRUFcXpwugXgJ8nvvLLWGBoPdqHal/K/81o8qdR+548375nRT4oleu3ZtBjrS/+29qXBRNeYf7iJTz0aA/a3Ohdgw1GAsKaMOCpkQy44bD6p9sxaVFe7KQc28+hdBODnxlB40pgLbHgU7MBdQPtnM8tAkBRXBTmFhLauAk3voKd8Go+odzSqQM1A6EMZ/l5DSlpL6I4Sjm28zs+WbYRv4atqVScxO7tm9i09RiBYS2549Ywju7ezwWgNOcMR9MU7ux9m7xIxDVRXA5yzp7g8PEUSqx2CnMzOJVRQqcHBtJKbu1+zXQ63CHKnkJJVhJrln7CjrRASllBwtpiCvMLaHTXf/hnYHXufuQRTizdzYafdlE5azc+rfoxtJd7XB4s9ENx2jj56zqWbculS887qBXgQq1zG0/fdz++WodzQwZV9cIlj72R6qLw/Em2bdmH1ccPl8OOqhow+VemzR330KK2P+Ag5cAOdh3Lwj+oCm1uv5MmNWTZMXFtVMVJbsoRftq8k2xHIP9o04Hud7TR/Hat7kpKWgghdEyGG4UQQsekpIUQQsekpIUQQsekpIUQQsekpIUQQsekpIUQQsekpIUQQsekpIUQQsf+DyL4jB79Nf0fAAAAAElFTkSuQmCC)
Triangles ABC and DEF above are similar. How much longer than segment EF is segment DE ?
Note:
There are three ways to prove that two triangles are similar- AAA,
SAS, SSS.
AAA means that the corresponding angles are equal,
SAS means two sides of the triangles are in equal ratio and the angles between these two sides are equal,
SSS means that all three corresponding sides have equal ratio