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

P=Perimeter

W=Width

L=Length

Assuming the 210 feet is the perimeter

P = 210 feet

P = 2W + 2L

W = 2/3 L . . . so sub W with 2/3 L in the equation

P = 2(2/3 L)+ 2(L) = 210 feet

4/3 L + 2L = 210 feet

10/3 L = 210 feet

Multiply both sides by 3/10 to solve for L

L = (210)(3/10) = 63 feet

W = 2/3 L so W = 2/3 x 63 = 42 feet

Garden is 42 feet wide by 63 feet long