Question

An architect designs a rectangular flower garden such that the width is exactly​ two-thirds of the length. If 210 feet of antique picket fencing are to be used to enclose the​ garden, find the dimensions of the garden.

Answer 1

Start by defining your variables.  Let the length be L and the width W. Note that W = 2L/3.

Use the Perimeter formula:  P = 2W + 2L.  Substituting,

P = 2[2L/3] + 2L, or P = 4L/3 + 2L, or   P = 4L/3 + 6L/3 = 10L/3 = 210 feet

Then 10L = 630 feet, and L = 63 feet.  Thus, W = 2L/3 = 2(63 feet)/3 = 42 feet.