A rectangular garden measures 8 feet by 7 feet. A path of uniform width is constructed around the garden. The path and the garden together cover an area of 132 ft². How wide is the path?

Answer 1

132 - 8(7) = 132 - 56 = 76 ft^2 for the walkway

76 = 2(8+2w)w) + 2w(7)

76 =4w^2 + 30w

4w^2 +30w - 76 = 0

2w^2 + 15w -38 = 0

w = -15/4 + (1/4)sqr(15^2 +8(38) =

w= 23/4 -15/4 = 8/4 =

2 feet in width

or another way to solve for width:

132 feet = (8+2w)(7+2w) = 56 + 30w + 4w^2

4w^2 + 30x - 76 = 0

2w^2 +15x - 38 = 0

x = -15/4 + (1/4)sqr(225 + 8(38)) = - 3.75 + .25(23) = 5.75-3.75 = 2 feet