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Question

A group of students were allotted a quadrilateral patch in the school campus to make a garden. They cleared up the patch and decided to grow medicinal plants. Find the area of the patch, if the dimensions are as given in the figure.

hint Hint:

Using pythagoras theorem, find the length of side AC.
area of patch ABCD = area of Δ ABC + area of Δ ADC
Find area of area of Δ ADC by heron's formula for finding the area of triangle

The correct answer is: 306 m2

Step1 :- Find the length of side Ac using pythagoras theorem,
In Δ ABC , AC² = AB² + BC²
We know that AB = 9 and BC = 40
Substituting the values we get AC² = 9² + 40² = 81+1600 = 1681 =41²
We get AC = 41 m
Step2:- Find the area of Δ ABC,
Here,Δ ABC is a right angle triangle .
Area of right angle triangle = ½ (product of lengths of perpendicular sides)
Area of Δ ABC = ½ (40 × 9)
Area of Δ ABC = 180 m²
Step 3:- Find the area of Δ ADC from heron's formula
Here, side length of triangle are 15,28 and 41 m
Heron's formula for area of triangle with side length
a,b,c are Area = $space square root of s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis end root$
Where s = $fraction numerator a plus b plus c over denominator 2 end fraction$
Let a = 28 ;b = 15 ;c = 41

We get s = $fraction numerator 28 plus 15 plus 41 over denominator 2 end fraction$ = 42
Area = $square root of 42 left parenthesis 42 minus 28 right parenthesis left parenthesis 42 minus 15 right parenthesis left parenthesis 42 minus 41 right parenthesis end root$
= $square root of 42 cross times 14 cross times 27 cross times I end root$
$square root of 15876 equals 126 straight m squared$
We get area of Δ ADC = 126 (m²)

Step 4:- Find the area of the Patch
area of patch ABCD = area of Δ ABC + area of Δ ADC
= 180 m²+ 126 m²
= 306 m²
Therefore area of patch ABCD = 306 m².

$P equals 215 left parenthesis 1.005 right parenthesis to the power of t over 3 end exponent$
The equation above can be used to model the population, in thousands, of a certain city t years after 2000. According to the model, the population is predicted to increase by 0.5% every n months. What is the value of n?

Note:
We need to understand what each quantity given in the equation $P equals 215 left parenthesis 1.005 right parenthesis to the power of t over 3 end exponent$
represents. For example, the population in year 2000 is 2,15,000. After 3 tears, that is, in year 2003, the population becomes $left parenthesis 215 cross times 1.005 right parenthesis$ thousand which is 216075.

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A group of students were allotted a quadrilateral patch in the school campus to make a garden. They cleared up the patch and decided to grow medicinal plants. Find the area of the patch, if the dimensions are as given in the figure.

Using pythagoras theorem, find the length of side AC.area of patch ABCD = area of Δ ABC + area of Δ ADCFind area of area of Δ ADC by heron's formula for finding the area of triangle

The correct answer is: 306 m2

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The equation above can be used to model the population, in thousands, of a certain city t years after 2000. According to the model, the population is predicted to increase by 0.5% every n months. What is the value of n?

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Using pythagoras theorem, find the length of side AC.
area of patch ABCD = area of Δ ABC + area of Δ ADC
Find area of area of Δ ADC by heron's formula for finding the area of triangle

Each co-ordinate (x, y) of the blue figure gets translated horizontally _ units and vertically _ units.

Each co-ordinate (x, y) of the blue figure gets translated horizontally _ units and vertically _ units.