Multiple choice

The area of a circle is equal to the area of a rectangle having perimeter 50 cm and length more than the breadth by 3 cm. What is the diameter of the circle?

  1. 7 cm

  2. 21 cm

  3. 28 cm

  4. 14 cm

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the breadth of the rectangle be B, so the length is B + 3. The perimeter is 2(L + B) = 50, which simplifies to 2B + 3 = 25, giving B = 11 cm and L = 14 cm. The area of the rectangle is 14 * 11 = 154 square centimeters. Since the area of the circle is also 154, we have pi * r^2 = 154, which yields r = 7 cm, and thus the diameter is 14 cm.

AI explanation

Let the breadth be x cm, so the length is x + 3 cm. The perimeter formula gives 2(x + x + 3) = 50, meaning x = 11. The area of the rectangle is 14 * 11 = 154 sq. cm, which equals the area of the circle. Using the area of a circle formula, pi * r^2 = 154, so r^2 = 154 / (22/7) = 49 and r = 7. The diameter is 2 * 7 = 14 cm.

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