Question

A rectangular garden has dimensions 3m by 4m. A path is built around the garden. The area of the garden and path is 6 times as a great as the area of the garden. What is the width of the path?

Answer 1

(3 + 2w) * (4 + 2w) = 3 * 4 * 6

4 w^2 + 14 w + 12 = 72 ... 2 w^2 + 7 w - 30 = 0

solve for w

Answer 2

Ag = Area of the garden.
Ap = Area of the path.

Ag + Ap = 6Ag.
3*4 + Ap = 6(3*4),
Ap = 60 sq. meters.

L*W = 60.
L/W = 4/3,
L = 4W/3,
4W/3 * W = 60,
4W^2 = 180,
W = ?