Question

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.

• A. 34 cm
• B. 26 cm
• C. 24 cm
• D. 16 m

Answer 1

Answer:

A. 34 cm

Let the length of the side of the square be x cm.

$x^2 = (x + 5) (x - 3)$

$x^2 = x^2 + 5x - 3x -15$

2x = 15

$x =\frac{15}{2}cm$

Now, length of the rectangle $=x+5=\frac{15}{2}+5=\frac{25}{2}cm$

and breadth $=\frac{15}{2}-3=\frac{15-6}{2}=\frac{9}{2}cm$

Required perimeter $= 2(\frac{25}{2}+\frac{9}{2})=2\times{\frac{34}{2}}$

$=34cm$