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

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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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