Question

A pair of adjacent sides of a rectangular and in the ratio $3:4$. If its diagonals is $20cm$ find the lengths of sides and hence the perimeter of the rectangle.

Answer 1

Let ratio be x.

$\begin{array}{c}b=3x\\ l=4x\\ in\Delta ABC\\ \angle B={90}^{\circ }\\ so,AB=4x\\ BC=x\\ AC=20\\ h^2=p^2=b^2\\ {\left(AC\right)}^2={\left(AB\right)}^2+{\left(BC\right)}^2\\ {\left(20\right)}^2={\left(4x\right)}^2+{\left(3x\right)}^2\\ 400=16x^2+9x^3\\ 400=25x^2\\ \frac{400}{25}=x^2\\ 16=x^2\\ x=4\\ b=4x=3\times 4=12\\ l=4x=4\times 4=16\\ Area=l\times b=12\times 16=192cm\\ P=2\left(l+b\right)=2\left(12+16\right)=56m\end{array}$