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: Option D
Solution(By Examveda Team)
Let the length of each side of the square be x cmThen, length of rectangle = (x + 5) cm and its breadth = (x - 3) cm
$$\eqalign{ & \therefore \left( {x + 5} \right)\left( {x - 3} \right) = {x^2} \cr & \Rightarrow {x^2} + 2x - 15 = {x^2} \cr & \Rightarrow x = \frac{{15}}{2} \cr} $$
∴ Length :
$$\eqalign{ & = \left( {\frac{{15}}{2} + 5} \right)cm \cr & = \frac{{25}}{2}cm \cr} $$
Breadth :
$$\eqalign{ & = \left( {\frac{{15}}{2} - 3} \right)cm \cr & = \frac{9}{2}cm \cr} $$
Hence, perimeter :
$$\eqalign{ & = 2\left( {l + b} \right) \cr & = 2\left( {\frac{{25}}{2} + \frac{9}{2}} \right)cm \cr & = 34\,cm \cr} $$
Related Questions on Area
A. 15360 m2
B. 153600 m2
C. 30720 m2
D. 307200 m2
E. None of these
A. 2%
B. 2.02%
C. 4%
D. 4.04%
E. None of these
A. 16 cm
B. 18 cm
C. 24 cm
D. Data inadequate
E. None of these
The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
A. 40%
B. 42%
C. 44%
D. 46%
Join The Discussion