SOLUTION: A rectangle is 9 cm longer than it is wide. The width is one seventh of the perimeter. What are the dimensions of the rectangle?

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Question 463491: A rectangle is 9 cm longer than it is wide. The width is one seventh of the perimeter. What are the dimensions of the rectangle?
Answer by htmentor(1343) (Show Source):
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A rectangle is 9 cm longer than it is wide. The width is one seventh of the perimeter. What are the dimensions of the rectangle?
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Let l = the length of the rectangle
Let w = the width of the rectangle
The length is 9 cm more than the width. In equation form this is:
l = w + 9 [1]
The width is 1/7 of the perimeter. Since the perimeter = 2l + 2w, we can write:
w = 1/7(2l + 2w) = 2/7(l + w) [2]
Substitute the value for l in [1] into [2]:
w = 2/7(w + 9 + w)
Solve for w:
w = 4/7w + 18/7
3/7w = 18/7
w = 6
Therefore the length, l = 6 + 9 = 15
Ans: w=6, l=15