If the length of a rectangle is decreased by 4 cm and the width is increased by 3 cm to make a square of the same area as the rectangle has, then find the perimeter of the rectangle.
Option:
A. 12 cm
B. 24 cm
C. 25 cm
D. 50 cm
Answer: D . 50 cm
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Justification:
Area of the rectangle A = L * B
Area of the square a = l * b => a = (L-4)*(B+3)
As, l = b => L - 4 = B + 3 => L - B = 7.
=> A = a => LB = LB + 3L -4B -12 => 3L - 4B = 12 => 3*(L-B)-B = 12
=> 3 * 7 - B = 12 => B = 9 = > L = 16
So, Perimeter of the rectangle P = 2 (L + B) = 2 * 25 = 50cm
