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

Answer: Option D

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