John is building a rectangular puppy kennel up against his house using 31 feet of fencing. the side against the house does not need a fence and the side parallel to his house needs to be 15 feet long. write an equation that models the situation and solve for the length of one of the shorter sides that extend out from the house.

John want to build a rectangular puppy kennel up against his house. The side against the house doesn't need a fence, so John still need to build 3 fences. He got 31 feet of fence. the fence parallel to the side against the house should be 15 feet long. So he still need to determine the side of the 2 other fences, which are equal because its a rectangular (the parallel sides in a rectangular are equal).
So the equation that models the situation is:
31 = 2s + 15, in which s represents the length of the one fence.

We need to solve for s. Let's subtract 15 from each side to have the variables on a side and the numbers on the other:
31 = 2s + 15
31 - 15 = 2s + 15 - 15
16 = 2s

Then divide both sides by 2 to have the variable s on a side and its value on the other:
16 = 2s
16/2 = (2s)/2
8 = s.

So the shorter sides of the rectangle needs to be 8 feet long each.

Let's check our
2s + 15 = 16 + 15 = 31.
Our answer has been approved.

Hope this helps! :D