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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.

Respuesta :

calculista

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

[tex]P=2(L+W)[/tex]

we have that

[tex]P=240\ ft[/tex]

so

[tex]240=2(L+W)[/tex]

Simplify

[tex]120=(L+W)[/tex] -----> equation A

[tex]W=\frac{2}{3}L[/tex] ----> equation B

Substitute equation B in equation A and solve for L

[tex]120=(L+\frac{2}{3}L)[/tex]

[tex]120=\frac{5}{3}L[/tex]

[tex]L=120(3)/5[/tex]

[tex]L=72\ ft[/tex]

Find the value of W

[tex]W=\frac{2}{3}(72)[/tex]

[tex]W=48\ ft[/tex]

therefore

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

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