OK. I did it, and I have the solution.
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The length of the deck is (5 + 2x) .
The width of the deck is   (4 + 2x) .

If the deck didn't have that big hole in the middle where the pool is,
then its area would be

   (5 + 2x) · (4 + 2x) .

When you multiply that all out, you get    Area = 4x² + 18x + 20

and the question tells us that the area of the whole big rectangle is 90 yds² .
So we can write

   4x² + 18x + 20 = 90 .

Subtract 90 from each side:    4x² + 18x - 70 = 0
Divide each side by 2 :    2x² + 9x - 35 = 0

You can use the quadratic equation to solve that and find out that
x = 2.5 yards, and that's what the question is asking you.
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That makes the deck 10 yds high and 9 yds wide.

Total area of the whole big rectangle, (deck + pool ), = 90 yds².

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3 years ago