**Re: Word Problem; Perimeter**
faith14 said:

I'm having problems with another world problem. A kitchen rug is 7 inches longer than its width. A bathroom rug has a width of 7 inches less that the kitchen rug but 3 inches longer. The perimeter of that bathroom rug is 106 inches. Find the dimensions of both rugs. I can't figure out if this is supposed to be two separate problems or what.

Let L = length; W = width:

Kitchen rug:

L =(W + 7)

W = (L - 7)

Bathroom rug:

W = (L - 14)

L = (W + 10)

perimeter (bathroom rug) = 2W + 2L = 106

2(L - 14) + 2(W + 10) = 106

2L - 28 + 2W + 20 = 106

2L + 2W -8 = 106

L + W - 4 = 53

L + W = 57

W = 57 - L <--- substitute this into either the kitchen or the bathroom equations to generate W and L

Bathroom:

57 - L = L - 14

71 = 2L

==> L = 35.5

W = 35.5 - 7

==> W = 28.5

Now use those two values and plug them back into each bathroom and kitchen L and W formula, to find the dimensions of each.