Question

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

Answer 1

In right angled $△ABC$,

${\left(3x\right)}^2+{\left(4x\right)}^2=4009x^2+16x^2=400\Rightarrow 25x^2=400x^2=16\Rightarrow x=4\therefore BC=12cmAB=16cm$$

Therefore perimeter of the rectangle

$=2(12+16)cm=2\times 28cm=56cm$