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A carpet was ordered with its length and width in the ratio 3:2. Later, the dimensions were changed so that the length and width were in the ratio 7:3, while the perimeter remained unchanged. What is the ratio of the areas of the carpet before and after the modification?

Mensuration MCQs for PPSC, FPSC, NTS, and Pakistan government job tests. Select an option below, then read the explanation.

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Subject
Mensurationmathematics-mcqs › mensuration
Published
10 Jul 2019
Last updated
28 May 2026

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Explanation

Let the original length and width be 3x and 2x respectively. For the modified carpet, let the dimensions be 7y and 3y. Since the perimeter remains the same: 2(3x + 2x) = 2(7y + 3y) which simplifies to 5x = 10y, so x = 2y. The ratio of areas is (3x * 2x) : (7y * 3y) = 6x^2 : 21y^2 = 6(2y)^2 : 21y^2 = 6 * 4y^2 : 21y^2 = 24y^2 : 21y^2 = 8 : 7.

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Practice related questions from the same subject.

  1. 1.A circle has a radius of 21 cm and a central angle measuring 135°. What is the perimeter of the corresponding sector?
  2. 2.A rectangle's length is two-fifths of the radius of a circle. The radius of this circle is equal to the side length of a square whose area measures 1225 square units. If the rectangle's breadth is 10 units, what is its area in square units?
  3. 3.Calculate the area of a rhombus with each side measuring 25 cm and one diagonal equal to 30 cm.
  4. 4.If the volumes of two cubes are in the ratio 729 to 1331, what is the ratio of their total surface areas?
  5. 5.A metal sphere with a radius of 12 cm is melted and reshaped into a cylindrical wire having a cross-sectional radius of 16 cm. What is the length of this wire?
  6. 6.Two cones have their volumes in the ratio 1 to 10, while their radii are in the ratio 1 to 2. What is the ratio of their heights?
  7. 7.A wheel has a radius of 22.4 cm. How far will the wheel travel after completing 500 full rotations?
  8. 8.A room measures 25 feet in length, 15 feet in width, and 12 feet in height. If the cost to whitewash the four walls is Rs. 5 per square foot, what will be the total expense given that the room has one door measuring 6 feet by 3 feet and three windows each measuring 4 feet by 3 feet?
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