Question

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

Answer 1

The diagonal of the rectangle is the hypotenuse of its sides.

Let the sides be $x,y$

The diagonal is $3x$

$⟹(3x{)}^2=x^2+y^{2}9x^2=x^2+y^2{y}^2=8x^{2}y=2\sqrt{2}x$

The ratio of sides are $x:2\sqrt{2}x=1:2\sqrt{2}$