A rancher has a fence that encloses a square pen with an area of 25 square meters. If the rancher uses this fence to enclose a circular antique rose garden, what will the area of the garden be?

Question

A rancher has a fence that encloses a square pen with an area of 25 square meters. If the rancher uses this fence to enclose a circular antique rose garden, what will the area of the garden be?

Answer 1

A rancher has a fence that encloses a square pen with an area of 25 square meters. If the rancher uses this fence to enclose a circular antique rose garden, what will the area of the garden be?

1. 25 m² = Area of square pen = (x)(x)=25; x² =25; so X = 5
2. The perimeter of the square pen = 4(X), so 4(5) = 20 m, you would use this as the length of fence to enclose the circular garden
3. Circumference (perimeter) of a circle = 2π(r) which = 20, so solve for r; 2π(r)=20; r = (20/2π) ≅3.18m
4. Use r (3.18 m) to determine area of garden, A=πr²
5. put in the 3.18 for r in the above and get A = 31.83 m²

Answer 2

The square is 5m x 5m

The perimeter is 20m.

C = 2πr

20 = 2πr

10 = πr

10 / π = r

A = πr²

A = π(10/π)²

A = 100 / π