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?

20 cm

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