Question

The diagonal of a rectangle is thrice its smaller side. Find the ratio of its sides.

Answer 1

Let AD = x cm
diagonal BD = 3x cm
In the right-angled triangle DAB,
$A{D}^2+A{B}^2=B{D}^2$ (Using Pythagoras Theorem)
$x^2+A{B}^2=(3x{)}^2$
$\Rightarrow x^2+A{B}^2=9x^2$
$\Rightarrow A{B}^2=9x^2-x^2$
$\Rightarrow A{B}^2=8x^2$
$\Rightarrow AB=2\sqrt{2}x$
Required ratio of AB : AD = $2\sqrt{2}x:x=2\sqrt{2}:1$