The length of a rectangle is three times of its width. If the length of the diagonal is $$8\sqrt {10} $$ cm, then the perimeter of the rectangle is :

A. $$15\sqrt {10} $$  cm

B. $$16\sqrt {10} $$  cm

C. $$24\sqrt {10} $$  cm

D. 64 cm

Answer: Option D

Solution(By Examveda Team)

Let breadth = x cm
Then, length = 3x cm
$$\eqalign{ & \Rightarrow {x^2} + {\left( {3x} \right)^2} = {\left( {8\sqrt {10} } \right)^2} \cr & \Rightarrow 10{x^2} = 640 \cr & \Rightarrow {x^2} = 64 \cr & \Rightarrow x = 8 \cr} $$
So, length = 24 cm and breadth = 8 cm
∴ Perimeter = [2(24 + 8)] cm = 64 cm