The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If…
2024
The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
- A.
22
- B.
18
- C.
25
- D.
26
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Correct answer: B
Solution:
Perimeter = 2(length + breadth). Given the ratio perimeter : breadth = 5 : 1, so 2(l + b)/b = 5, which gives 2(l + b) = 5b.
Simplify: 2l + 2b = 5b ⇒ 2l = 3b ⇒ b = (2/3)l.
Area = l × b = l × (2/3)l = (2/3)l². Set this equal to 216: (2/3)l² = 216 ⇒ l² = 216 × (3/2) = 324.
Therefore l = √324 = 18 cm. Then b = (2/3) × 18 = 12 cm. Check: Perimeter = 2(18 + 12) = 60 and 60 : 12 = 5 : 1, so the solution is consistent.
Answer: 18 cm