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?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e 20 cm.
Concept Used:
Area of rectangle = l × b
Area of square = a2
Perimeter of rectangle = 2(l + b)
Explanation:
Let the length and breadth of the given rectangle be l cm and b cm respectively.
According to the given question, side of square = l - 4 = b +2
Now, l = b + 6 ....(i)
Also, Area of square = area of rectangle
⇒ (l - 4)(b + 2) = lb
⇒ lb + 2l - 4b - 8 = lb
⇒ 2(l - 2b) = 8
⇒ l - 2b = 4 ...(ii)
Using the values in equation (i) in equation (ii), we get
(b + 6) - 2b = 4
⇒ 6 - b = 4
⇒ b = 2 cm
Now, from equation (i), l = 2 + 6 = 8 cm
So, the perimeter of rectangle = 2(8 + 2) = 20 cm.