Question

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

Answer 1

Let the sides be $3x,4x$ (in cm).
Area = $\frac{1}{2}\left(3x\right)\left(4x\right)=1014⟹x^2=169⟹x=13$
Let the length of hypotenuse be $c$.
According to Pythagorus' Theorem, $c^2=(3x{)}^2+(4x{)}^2$
$⟹c^2=25x^2⟹c=5x=5\cdot 13=65\text{cm}$