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Question

The sides of a triangular plot are in the ratio of 16: 8: 10 and its perimeter is 340 m. Its area in m2 is 100A. The value of A is

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Solution

Let the sides of the triangle be 16x, 8x and 10x.

Then, 16x + 8x + 10x = 340
34x = 340
x = 34034
x =10.

Hence the sides are 160 cm, 80 cm and 100 cm.
Using the Heron's formula, Area A = s(sa)(sb)(sc)

Semi-Perimeter s = perimeter2
=3402
=170cm

A=170(170160)(170100)(17080)
=170×10×70×90
=1001071cm2

The value of A is 1071


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