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Maths-

General

Easy

Question

Sides of a triangle are in the ratio 12 : 17 : 25 and its perimeter is 540 cm. Find its area.

hint Hint:

Let sides of triangle be 12x , 17x and 25x

The correct answer is: 9000 cm2

It is given that Perimeter of triangle = 540 cm
⇒ 12x + 17x + 25x = 540
⇒ 54x = 540
⇒ x = 10
So, a = 120 cm , b = 170 cm , c = 250 cm
Using Heron’s formula,
Area of triangle = $square root of s left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis end root$ where s = $fraction numerator a plus b plus c over denominator 2 end fraction$
s = $540 over 2$ = 270
Area of triangle
= $square root of 270 left parenthesis 270 minus 120 right parenthesis left parenthesis 270 minus 170 right parenthesis left parenthesis 270 minus 250 right parenthesis end root$
= $square root of 270 left parenthesis 150 right parenthesis left parenthesis 100 right parenthesis left parenthesis 20 right parenthesis end root$
= 9000 cm²

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