The sides of a triangle having area $7776 s q . c m$ are in the ratio $3 : 4 : 5$ . The perimeter of the triangle is

400 c m

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412 c m

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424 c m

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432 c m

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Solution

The correct option is D $432 c m$
$A r e a = 7776 c m^{2}$
Its sides are $3 x, 4 x$ and $5 x$ .
Semi perimeter $= \frac{3 x + 4 x + 5 x}{2} = 6 x$
$7776 = \sqrt{6 x (3 x) (2 x) x}$
$7776 = 6 \times x^{2}$
$x^{2} = 1296$
$x = 36$
$∴$ Sides are $= 108, 144, 180$
Hence, perimeter is $432 c m$ .

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