The sides of a rectangular field are 198 m and 175 m long. Its area is equal…

Concept

When two plane figures have equal areas, equate their area formulas. For a rectangle, A = l × b; for a circle, A = πr2, and the circle’s perimeter (circumference) is C = 2πr.

The shared area determines r first; the circumference is then obtained from that radius.

Application

1. Calculate the rectangle’s area: A = 198 × 175 = 34,650 m2.

2. Equate the areas: πr2 = 34,650. With π = 22/7, r2 = 34,650 × 7/22 = 11,025.

3. Take the positive square root because radius is a length: r = √11,025 = 105 m.

4. Calculate the circumference: C = 2 × 22/7 × 105 = 660 m.

Cross-check

For r = 105 m, the circle’s area is (22/7) × 1052 = 34,650 m2, exactly equal to 198 × 175. Therefore, the required perimeter is 660 m.