SOLUTION: The width of a rectangle is 1 foot shorter than half the length. If the perimeter of the rectangle is 64 feet find the dimensions of the rectangle.

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Question 674518: The width of a rectangle is 1 foot shorter than half the length. If the perimeter of the rectangle is 64 feet find the dimensions of the rectangle.
Answer by jokaehler(26) About Me  (Show Source):
You can put this solution on YOUR website!
With this question, break down the sentence into bits and pieces.
"The width of a rectangle is..."
w =

"1 foot shorter than half the length."
+1%2F2+ l - 1

"If the perimeter of the rectangle is 64 feet..."
P = 64
(NOTE: Remember P = 2l + 2w)

"Find the dimensions of the rectangle."
Find "l" and "w."

Now that we have those, we piece it all together.
w = +1%2F2+ l - 1
P = 2l + 2w
64 = 2l + 2(+1%2F2+ l - 1)

Use the distributive property.
64 = 2l + l - 2

Combine like terms, and add two to both sides.
66 = 3l

Divide both sides by 3.
22 = l

Now that we have "l," we can find "w" by plugging it into w = +1%2F2+ l - 1.
+1%2F2+ * 22 - 1

Solve.
11 - 1 = 10


length = 22
width = 10


Check your work.

P = 2l + 2w
64 = (2 * 22) + (2 * 10)
64 = 44 + 20
64 = 64