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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.

A34 cm

B26 cm

C24 cm

D16 m

Answer:

A. 34 cm

Read Explanation:

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

x2=(x+5)(x3)x^2 = (x + 5) (x - 3)

x2=x2+5x3x15x^2 = x^2 + 5x - 3x -15

2x = 15

x=152cm x =\frac{15}{2}cm

Now, length of the rectangle =x+5=152+5=252cm=x+5=\frac{15}{2}+5=\frac{25}{2}cm

and breadth =1523=1562=92cm=\frac{15}{2}-3=\frac{15-6}{2}=\frac{9}{2}cm

Required perimeter =2(252+92)=2×342= 2(\frac{25}{2}+\frac{9}{2})=2\times{\frac{34}{2}}

=34cm=34cm


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