A Rectangular Garden

Question

A rectangular garden must have a perimeter of 145 feet and an area of at least 1100 square feet. Describe the possible lengths of the garden. Round your answers to the nearest foot.

Answer 1

biggest area would be a square with length = width = about 36 feet each

but rectangles with 51 x 22 would also have perimeter = about 145 feet and area > 1100 sqr. ft.

LW = minimum 1100

Perimeter = 145 = 2(L+W)

L+W = 145/2

L = 145/2 -W

Area = LW = (145/2-W)W = (145/2)W - W^2 = 1100

solve the quadratic to get two solutions: 51 and 22