If the length of certain rectangle is decreased by 4 cm and breadth is increased by 2 cm, it would result in a square of the same area. What is the perimeter of the original rectangle?
Answer & explanation
Correct answer: option 3
We know that,
Area of rectangle = L × B
Area of square = Side × Side
Perimeter of rectangle = 2(L + B)
Let length = L and breadth = B,
The sides of the square are equal,
= L − 4 = B + 2 ...........(1)
= L = B + 6
The area of the rectangle is equal to the area of the square,
L × B = (L - 4)(B + 2)
= (B + 6)(B) = (B + 6 - 4)(B + 2)
= B2 + 6B = (B + 2)2
= B2 + 6B = B2 + 4B + 4
= 6B = 4B + 4
= B = 2 cm
then form (1) we get,
= L - 4 = B + 2
= L - 4 = 2 + 2
= L = 4 + 4 = 8 cm
Now the Perimeter of the rectangle,
= P = 2(8 + 2) = 2(10) = 20 cm