Question

An architect designs a rectangular flower garden such that the width is exactly two-thirds if the length. If 240 feet of antique picket fencing are being used to enclose the garden, find the dimensions of the garden.

Answer 1

Answer:

The length of the rectangular flower garden is 72 feet and the width is 48 feet

Step-by-step explanation:

Let

L ----> the length of the rectangular flower garden in feet

W ---> the width of the rectangular flower garden in feet

we know that

The perimeter of the rectangular flower garden is

$P=2(L+W)$

we have that

$P=240\ ft$

so

$240=2(L+W)$

Simplify

$120=(L+W)$ -----> equation A

$W=\frac{2}{3}L$ ----> equation B

Substitute equation B in equation A and solve for L

$120=(L+\frac{2}{3}L)$

$120=\frac{5}{3}L$

$L=120(3)/5$

$L=72\ ft$

Find the value of W

$W=\frac{2}{3}(72)$

$W=48\ ft$

therefore

The length of the rectangular flower garden is 72 feet and the width is 48 feet