# Word Problem; Perimeters of two rugs

#### faith14

##### New member
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.

The variables for the kitchen rug I think would be 2(x) + 2(x + 7) for the width and length. Should the equation for the bathroom rug be 2(x - 7) + 3 = 106? I don't know what the next step is or if I'm messing this one up and that's the reason I'm stuck. Should the equation also contain the kitchen rug formula.

Thanks!

#### jwpaine

##### Full Member
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.

#### faith14

##### New member
Re: Word Problem; Perimeter

Thanks again!