Question

An architect designs a rectangular flower garden such that the width is exactly​ two-thirds of the length. if 410 feet of antique picket fencing are to be used to enclose the​ garden, find the dimensions of the garden.

Answer 1

width = 82 feet, length = 123 feet

First, write down equations that express what you've been given.

w = 2/3 l

p = 410

p = 2(w+l)

Since we have an expression that defines w in terms of l, substitute for w, the expression. Also substitute the known value for p in the expression.

p = 2(w + l)

410 = 2( 2/3 l + l)

Combine the l terms

410 = 2( 5/3 l)

Multiply

410 = 10/3 l

Multiple both sides by 3

1230 = 10 l

Divide both sides by 10

123 = l

So we now know the length is 123 feet. So plug in the known value of l into the formula w = 2/3 l to get the width w = 2/3 123 = 82