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:

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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