The areas of a square and a rectangle are equal. The length of the rectangle is greater than the length of any side of the square by 5 cm and the breadth is less by 3 cm. Find the perimeter of the rectangle ?

Answer: Option D

Let the length of each side of the square be x cm
Then, length of rectangle = (x + 5) cm and its breadth = (x - 3) cm
$$\begin{array}{rl}& \therefore \left(x+5\right)\left(x-3\right)=x^2\\ & \Rightarrow x^2+2x-15=x^2\\ & \Rightarrow x=\frac{15}{2}\end{array}$$
∴ Length :
$$\begin{array}{rl}& =\left(\frac{15}{2}+5\right)cm\\ & =\frac{25}{2}cm\end{array}$$
Breadth :
$$\begin{array}{rl}& =\left(\frac{15}{2}-3\right)cm\\ & =\frac{9}{2}cm\end{array}$$
Hence, perimeter :
$$\begin{array}{rl}& =2\left(l+b\right)\\ & =2\left(\frac{25}{2}+\frac{9}{2}\right)cm\\ & =34cm\end{array}$$