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.

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.