Question

the sides of a triangular plot are in the ratio of 3 : 5 : 7: and its perimeter is 300 m find its area

Answer 1

let the Ratio be in x
thus the sides are 3x 5x and 7x
perimeter of Triangle = sum of all the sides
300 = 3x + 5x + 7x
300 = 15x
x = 300/15
x = 20

the sides of the triangle are 60(3x) , 100(5x) and 140(7x)

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Answer 2

Given ratio of the sides 3 : 5 : 7

Let x be the constant ratio:

3x + 5x + 7x = 300

15x = 300

x = 300 ÷ 15

x = 20

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Find the sides length:

3x = 3 x 20 = 60 m

5x = 5 x 20 = 100 m

7x = 7 x 20 = 140 m

The length of the sides are 60 m, 100 m and 140 m

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Formula to find the area:

$\text {Area = } \sqrt{p( p - a) (p - b) ( b- c)}$

$\text { . . . . . . where P} = \dfrac{a + b + c }{2}$

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Find P:

$p = \dfrac{300}{2} = 150$

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FInd Area:

$\text {Area = } \sqrt{150( 150 - 60) ( 150 - 100) (150 - 140)} = 2598 \text { m}^2$

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Answer: Area = 2598 m²