Question

The sides (other then hypotenuse) of a right triangle are in the ratio $3:4$. A rectangle, the hypotenuse being the longer side of the rectangle. The breadth of the rectangle is four-fifth of its length. Find the shortest side of the right triangle, if the perimeter of the rectangle is $180cm$.

Answer 1

Perpendicular sides of triangle are in ratio of $3:4$ so,

Let is $\perp ar$ sides be $3x$ and $4x$

$l$=length of rectangle

$b$=breadth of rectangle

$\begin{array}{c}l=\sqrt{{\left(4x\right)}^2+{\left(3x\right)}^2}=5x\\ b=\frac{4}{5}l=\frac{4}{5}\times 6x=4x\end{array}$

Perimeter of rectangle $=2\left(l+b\right)=180cm$

$\begin{array}{c}\Rightarrow 2\left(4x+5x\right)=180cm\\ \therefore x=10cm\end{array}$

Shortest side of triangle is $3x$

$=3\times 10=30cm$