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Applications (Word Problem)

The legs of a...

Question

The legs of a right triangle are in the ratio 3 : 4 and its area is 1014 $c m^{2}$ . Find the lengths of its legs .

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Solution

Let the legs be $3 x$ and $4 x$

Then,
$\frac{1}{2} \times 12 x^{2} = 1014$

$6 x^{2} = 1014$
$x^{2} = 169$
$x = 13$

Therefore, length of legs is $3 x = 3 \times 13 = 39$ cm and $4 x = 4 \times 13 = 52$ cm.

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