Question

The sides of a triangular plot are in the ratio of 16: 8: 10 and its perimeter is 340 m. Its area in $m^2$ is $100\sqrt{A}$. The value of A is

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Answer 1

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

Then, 16x + 8x + 10x = 340
$\Rightarrow$ 34x = 340
$\Rightarrow$ x = $\frac{340}{34}$
$\Rightarrow$ x =10.

Hence the sides are 160 cm, 80 cm and 100 cm.
Using the Heron's formula, Area A = $\sqrt{s(s-a)(s-b)(s-c)}$

Semi-Perimeter s = $\frac{\text{perimeter}}{2}$
$=\frac{340}{2}$
$=170cm$

$\therefore A=\sqrt{170(170-160)(170-100)(170-80)}$
$=\sqrt{170\times 10\times 70\times 90}$
$=100\sqrt{1071}c{m}^2$

The value of A is 1071