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. 17 cm
• B. 26 cm
• C. 30 cm
• D. 34 cm

Answer 1

Answer:

D. 34 cm

areas of a square and a rectangle are equal.

$a^2=L\times{B}$

length of the rectangle is greater than the length of any side of the square by 5 cm and breadth is less by 3 cm

$L=a+5$

$B=a-3$

$a^2=(a+5)\times{(a-3)}$

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

$2a=15$

$a=\frac{15}{2}$

$L=\frac{15}{2}+5=\frac{25}{2}$

$B=\frac{15}{2}-3=\frac{9}{2}$

Perimeter of Rectangle = $2(L+B)$

$=2(\frac{25}{2}+\frac{9}{2})$

$=2\times{\frac{34}{2}}$

$=34cm$