SOLUTION: A rectangular swimming pool is 8 meters long and 12 meters wide. A tile border of uniform width is to be built around the pool using 120 square meters of tile. How wide shoul

Question 11388: A rectangular swimming pool is 8 meters long and 12 meters wide. A tile border of uniform width is to be built around the pool using 120 square meters of tile. How wide should the boarder be ?

Answer by prince_abubu(198) (Show Source): You can put this solution on YOUR website!
Let's say that w is the width of the border. If the border is the same width all around the pool (on all four sides), then you'd automatically add 2 widths to both length and width of the swimming pool. So, the extended length is 12 + 2w, because there are two w's, one for each long side. The extended width is 8 + 2w, because there are two w's, one for each shorter side.

<-------- This is the expression for the total area of the rectangle including the borders AND the swimming pool. Since we want only the area of the border, we will have to subtract the area of the swimming pool from this product.

<----- Much better. The area of the extended rectangle (with the border) MINUS the area of the swimming pool (the 96 square meters) should leave us with the area of the border, which is 120 square meters.

<-------- FOILed

<------- The 96's cancel

<--------- The 24w and 16w combine because they are like terms.

<----- re-ordered the terms because it looks better this way.

<------- subtracted 120 from both sides so that the right side will be zero. We do this so that we can solve the quadratic equation.

<------ divided both sides (or all terms) by 4.

We are going to have to use the quadratic formula to solve this because it looks unfactorable. Just for review, the quadratic formula is . In our case, a = 1, b = 10, and c = -30. Let's plug it in:

<------ simplified

<----- simplified further

<------ simplified further.

We will throw out the option since that obviously forces our answer to be negative. We can't have a negative answer because measurements can't be negative. We'll keep the solution, which turns out to be 2.416 meters. The width of the border should be about 2.416 meters.

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