The ratio of length and breadth of a rectangle is 5 : 4. The perimeter of rectangle is 54 cm. Find the area of rectangle.

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RRB NTPC Exam 27 Jan 2021 click here to view all questions

The ratio of length and breadth of a rectangle is 5 : 4. The perimeter of rectangle is 54 cm. Find the area of rectangle.

A180 cm2

B160 cm2

C210 cm2

D280 cm2

Akhilesh ? Apr 1 '25 at 20:39

correct answer is: option a [180 cm2]
Explanation: Let the length of the rectangle be \(5x\) cm and the breadth be \(4x\) cm.
The perimeter of the rectangle is given by \(2(l+b)\). Therefore, \(2(5x+4x) = 54\).
This simplifies to \(2(9x) = 54\), or \(18x = 54\).
Dividing both sides by 18, we get \(x = 3\).
Thus, the length is \(5x = 5 \times 3 = 15\) cm and the breadth is \(4x = 4 \times 3 = 12\) cm.
The area of the rectangle is given by \(l \times b = 15 \times 12 = 180\) cm².

• Option a: Correct, as the area is calculated to be 180 cm².
• Option b: Incorrect, the area is not 160 cm².
• Option c: Incorrect, the area is not 210 cm².
• Option d: Incorrect, the area is not 280 cm².

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correct answer is: option a [180 cm2] Explanation: Let the length of the rectangle be \(5x\) cm and the breadth be \(4x\) cm. The perimeter of the rectangle is given by \(2(l+b)\). Therefore, \(2(5x+4x) = 54\). This simplifies to \(2(9x) = 54\), or \(18x = 54\). Dividing both sides by 18, we get \(x = 3\). Thus, the length is \(5x = 5 \times 3 = 15\) cm and the breadth is \(4x = 4 \times 3 = 12\) cm. The area of the rectangle is given by \(l \times b = 15 \times 12 = 180\) cm2. Option a: Correct, as the area is calculated to be 180 cm2. Option b: Incorrect, the area is not 160 cm2. Option c: Incorrect, the area is not 210 cm2. Option d: Incorrect, the area is not 280 cm2. Akhilesh ? answered Apr 1 '25 at 20:39

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