The length of the rectangle is three times its breadth. If its length is decreased by 7cm and breadth is increased by 7cm, its area is increased by 21cm2. The length of the first rectangle is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e.15 cm.
Let, the breadth be a and the length be 3a
So, the area of the rectangle = length × breadth = 3a × a = 3a2
Now,
The length is decreased by 7cm = (3a - 7) and,
The breadth is increased by 7cm = (a + 7)
and, its area is increased by 21cm2 = (3a2 + 21)
Area of the new rectangle = new length × new breadth
⇒ (3a2 + 21) = (3a - 7) × (a + 7)
⇒ 3a2 + 21 = 3a2 + 21a - 7a - 49
⇒ 21 = 14a - 49
⇒ 70 = 14a
⇒ a = 5
Hence, the length = 3a = 15 cm