Question
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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 100√A. The value of A is
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Answer: Option A
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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(s−a)(s−b)(s−c)
Semi-Perimeter s = perimeter2
=3402
=170cm
∴A=√170(170−160)(170−100)(170−80)
=√170×10×70×90
=100√1071cm2
The value of A is 1071
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