A circular wire of diameter 70 cm is cut and bent to form a rectangle whose sides are in the ratio 4 : 7. 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) → 40 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 the wire \(\displaystyle=\frac{22}{7}\times70=220\) cm
Sides \(4k\) and \(7k\): perimeter \(=2(4k+7k)=22k\)
\(22k=220\), so \(k=10\)
Smaller side \(=4\times10=40\) cm (the other side is 70 cm)
