A circular wire with a radius of 42 cm is reshaped into a rectangle where the length and width are in the ratio 6:5. What is the length of the shorter side of the rectangle?

Explanation

The circumference of the original circle is 2 × π × 42 = 264 cm. This becomes the perimeter of the rectangle. Let the shorter side be 5x and the longer side be 6x. The perimeter is 2 × (5x + 6x) = 22x, which equals 264 cm. Solving for x gives x = 12 cm. Therefore, the shorter side is 5x = 60 cm.