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Question

The sides of a triangle are in the ratio 13 : 14 : 15 and its perimeter is 84 cm. Find the area of the triangle.

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Solution

Let the sides of the triangle be 13x cm, 14x cm and 15x cm.
Perimeter = Sum of all sides
or, 84 = 13x + 14x + 15x
or, 42x = 84
or, x = 2
So, sides of the triangle are 13×2, 14×2 and 15×2, i.e., 26 cm, 28 cm and 30 cm.
Let:a=26 cm, b = 28 cm and c=30 cms= 842=42 cmBy Heron's formula, we have:Area of the triangle=s(s-a)(s-b)(s-c)=42(42-26)(42-28)(42-30)=42×16×14×12=14×3×4×4×14×3×2×2=14×3×4×2=336 cm2

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Area of a Triangle - by Heron's Formula
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