Question

The sides of a triangle having area $7776sq.cm$ are in the ratio $3:4:5$. The perimeter of the triangle is

• A. $400cm$
• B. $412cm$
• C. $424cm$
• D. $432cm$

Answer 1

The correct option is D $432cm$

$Area=7776c{m}^2$
Its sides are $3x,4x$ and $5x$.
Semi perimeter $=\frac{3x+4x+5x}{2}=6x$
$7776=\sqrt{6x\left(3x\right)\left(2x\right)x}$
$7776=6\times x^2$
$x^2=1296$
$x=36$
$\therefore$ Sides are $=108,144,180$
Hence, perimeter is $432cm$.