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

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

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=(2)/(3)L` ----> equation B

Substitute equation B in equation A and solve for L

`120=(L+(2)/(3)L)`

`120=(5)/(3)L`

`L=120(3)/5`

`L=72\ ft`

Find the value of W

`W=(2)/(3)(72)`

`W=48\ ft`

therefore

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