SOLUTION: The length of a rectangular garden is 8 feet longer than its width. If the garden's perimeter is 180 feet, what is the area of the garden in square feet?

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Question 212246: The length of a rectangular garden is 8 feet longer than its width. If the garden's perimeter is 180 feet, what is the area of the garden in square feet?

Found 2 solutions by rfer, drj:
Answer by rfer(12657) About Me  (Show Source):
You can put this solution on YOUR website!
2(x+8)+2x=180
2x+16+2x=180
4x=164
x=41
x+8=49
---------------
a=lw
a=49*41
a=2009 sq ft

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a rectangular garden is 8 feet longer than its width. If the garden's perimeter is 180 feet, what is the area of the garden in square feet?

Step 1. Let w be the width of the rectangular garden.

Step 2. Let w+8 be the length of the rectangular garden.

Step 3. Let P be the perimeter of the rectangular garden.

Step 4. P=2(w+w+8) since we have 2w plus 2(w+8) be lengths of the 4 sides. A rectangular perimeter is adding the four lengths of the sides of a rectangle.

P=2%282w%2B8%29=4w%2B16=180

Divide by four on both sides of equation to yield

%284w%2B16%29%2F4=180%2F4

w%2B4=45
w=41
w%2B8=49


Step 5. Area is length times width for a rectangle.

A=w%28w%2B8%29

Substituting w=41 and w+8=49 into A yields

A=%2841%29%2849%29=2009

ANSWER: Area A=2009

Hope this helps and good luck in the future! Dr J

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