Multiple choice

A circular wire of radius 28 cm is bent in the form of a rectangle, whose length and breadth are in the ratio 7 : 4. What is the area of the rectangle?

  1. 1816 sq cm

  2. 1572 sq cm

  3. 1792 sq cm

  4. 1652 sq cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Circumference = 2 * pi * 28 = 176. Perimeter of rectangle = 2(L+B) = 176, so L+B = 88. Ratio 7:4 means L=7x, B=4x. 11x = 88, so x = 8. L = 56, B = 32. Area = 56 * 32 = 1792.

AI explanation

The circumference of the circular wire is 2 times pi times the radius, giving 2 times (22 divided by 7) times 28, which equals 176 cm. This length becomes the perimeter of the rectangle, so 2 times the sum of length and breadth equals 176, meaning the sum of length and breadth is 88 cm. Using the given ratio of 7 to 4, the length is (7 divided by 11) times 88, which is 56 cm, and the breadth is (4 divided by 11) times 88, which is 32 cm. The area of the rectangle is length times breadth, resulting in 56 times 32, equal to 1792 sq cm.

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