A circular wire of diameter 112 cm is cut and bent to form a rectangle whose sides are in the ratio 5 : 11. What is the length of the smaller side of the rectangle? (Take \(\pi=\frac{22}{7}\))
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 55 cm
Bending does not change the length of the wire, so the perimeter of the rectangle equals the circumference of the circle, \(\pi d\).
Length of wire \(\displaystyle =\frac{22}{7}\times112=352\) cm
Sides \(5k\) and \(11k\): perimeter \(=2(5k+11k)=32k\)
\(32k=352\), so \(k=11\)
Smaller side \(=5\times11=55\) cm
