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Jim is enclosing a rectangular garden with 170 feet of fencing. The length of the garden is 10 feet more than twice it’s width, w. Determine the area of the garden, in sqaure feet. Use an algebraic approach to model the problem.

Respuesta :

calculista

Answer:

[tex]1,500\ ft^2[/tex]

Step-by-step explanation:

Let

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

w ---> the width of  the rectangular garden in feet

step 1

Find the width

we know that

The perimeter of the rectangular garden is

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

[tex]P=170\ ft[/tex]

so

[tex]170=2(L+W)[/tex]

Simplify

[tex]85=(L+W)[/tex] ----> equation A

[tex]L=2W+10[/tex] ----> equation B

substitute equation B in equation A and solve for W

[tex]85=(2W+10+W)[/tex]

[tex]85-10=3W[/tex]

[tex]3W=75[/tex]

[tex]W=25\ ft[/tex]

Find the value of L

[tex]L=2(25)+10=60\ ft[/tex]

step 2

Find the area

we know that

The area of the rectangular garden is

[tex]A=(LW)[/tex]

substitute the values

[tex]A=(60)(25)=1,500\ ft^2[/tex]

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