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If the perimeter of a rectangle is 18 inches and one side is one inch shorter than the other how long are the sides

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Start with appropriate representations:  L = length and W = width.  Then W = L - 1.

The perimeter is P = 18 in = 2L + 2W, which here would be:

                                  18 in = 2L + 2(L - 1), or   18 in = 4L -2.  Solving for L:

                                                                         20 in = 4L, and L = 5 in.

Then W = 5 in - 1 in = 4 in.

Note that 2W + 2L does come to 18 in here:  2(5 in) + 2(4in) = 18 in.

The side lengths are 4 and 5 inches, respectively.