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Maths-

General

Easy

Question

The perimeter of the triangle is 44cm. if its sides are in the ratio 9:7:6. Find its area.

hint Hint:

Let sides of the triangle be a = 9x , b = 7x and c = 6x

The correct answer is: 8√110 cm2

It is given that perimeter of the triangle = 44cm
i.e. Sum of all sides = 44 cm
9x + 7x + 6x = 44 ⇒ 22x = 44 ⇒ x = 2
So, a = 18 cm , b = 14 cm and c = 12 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 = $44 over 2$ = 22
Area of triangle = $square root of 22 left parenthesis 22 minus 18 right parenthesis left parenthesis 22 minus 14 right parenthesis left parenthesis 22 minus 12 right parenthesis end root$
= $square root of 22 left parenthesis 4 right parenthesis left parenthesis 8 right parenthesis left parenthesis 10 right parenthesis end root$
= $square root of left parenthesis 2 right parenthesis left parenthesis 11 right parenthesis left parenthesis 4 right parenthesis left parenthesis 8 right parenthesis left parenthesis 10 right parenthesis end root equals 8 square root of 110 cm squared$

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