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Question

The sides of an equilateral triangle are shortened by 12 units, 13 units and 14 units respectively and a right-angle triangle is formed. Find the length of the side of the equilateral triangle?

hint Hint:

Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.
If a is the perpendicular, b is the base, and c is the hypotenuse, then according to the definition, the Pythagoras Theorem formula is given as
c2= a2 + b2

The correct answer is: the length of the side of the equilateral triangle is 17 cm

Let’s say that the length of the sides of the equilateral triangle is l
It is given that the sides of an equilateral triangle are shortened by 12 units, 13 units and 14 units and a right-angle triangle is formed. So, the new sides of the right-angled triangle are l-12, l-13 and l-14, in which the longest side “l-12” will be the hypotenuse of the right-angled triangle and the other two will be the perpendicular and base.
Using Pythagoras theorem:
hypotenuse² = perpendicular² + base²
(l-12)² =(l-13)² + (l-14)²
l² -24l + 144 = l² -26l + 169 + l² -28l + 196
l² -30l + 221 = 0
Using quadratic formula
l = $fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction$
a = 1, b = -30, c = 221
l = $fraction numerator 30 plus-or-minus square root of 30 squared minus 4 cross times 1 cross times left parenthesis 221 right parenthesis end root over denominator 2 cross times 1 end fraction$
l = $fraction numerator 30 plus-or-minus square root of 16 over denominator 2 end fraction$
l = $fraction numerator 30 plus-or-minus 4 over denominator 2 end fraction$ = $fraction numerator 30 plus 4 over denominator 2 end fraction$ = 17 cm
Final Answer:
Hence, the length of the side of the equilateral triangle is 17 cm.

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The sides of an equilateral triangle are shortened by 12 units, 13 units and 14 units respectively and a right-angle triangle is formed. Find the length of the side of the equilateral triangle?

The correct answer is: the length of the side of the equilateral triangle is 17 cm

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Identify proper noun th the following sentence
"Kk Menon was a legendary singer".

Identify proper noun th the following sentence
"Kk Menon was a legendary singer".

Solve the inequality and graph the solution:
x+8>11

Solve the inequality and graph the solution:
x+8>11

Choose the use of Simple future Tense.
1) An action that takes place in the future
2) An action as it goes on in the future or action planned for some time in the future

Choose the use of Simple future Tense.
1) An action that takes place in the future
2) An action as it goes on in the future or action planned for some time in the future