Multiple choice

A circular wire of diameter $42 cm$ is bent in the form of a rectangle whose sides are in the ratio $6 : 5$. The area of the rectangle is $\displaystyle \left ( \pi =\frac{22}{7} \right )$

  1. $540 \displaystyle cm^{2}$
  2. $1080 \displaystyle cm^{2}$
  3. $2160 \displaystyle cm^{2}$
  4. $4320 \displaystyle cm^{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Circumference = 2 * pi * r = pi * d = 22/7 * 42 = 132. Perimeter of rectangle = 2(l+w) = 132, so l+w = 66. Ratio 6:5 means 6x + 5x = 66, so 11x = 66, x = 6. Sides are 36 and 30. Area = 36 * 30 = 1080.

AI explanation

The wire is bent into a rectangle, so the circumference of 42 pi becomes the perimeter of the rectangle, and using pi equals 22/7 gives 132 cm. If the sides are 6x and 5x, the perimeter is 22x, making x equal to 6 and the sides 36 cm and 30 cm. Multiplying 36 by 30 gives the area as 1080 cm squared.