Question : If the length of a 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?
Option 1: 15 cm
Option 2: 24 cm
Option 3: 20 cm
Option 4: 10 cm
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Correct Answer: 20 cm
Solution :
Let length be L and breadth be B,
Since 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)
⇒ B
2
+ 6B = (B + 2)
2
⇒ B
2
+ 6B = B
2
+ 4B + 4
⇒ 6B = 4B + 4
⇒ 2B = 4
⇒ B = 2 cm
Then from (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)
⇒ P = 2(10) = 20 cm
The perimeter of the original rectangle is 20 cm.
Hence, the correct answer is 20 cm.
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