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.
Answer: 36
Step-by-step explanation:
8-2+30
6+30
36
X = 101 + 41
x = 142
hope it helps
Check the picture below.
let's notice the "white" ∡1 is an inscribed angle with an intercepted arc of (x-32), and the "green" ∡5 is also an inscribed angle with an intercepted arc of (2x).
the ∡6 and ∡2 are both external angles, however they intercepted two arcs, a "far arc" and a "near arc", thus we'll use the far arc - near arc formula, as you see in the picture, and we'll use the inscribed angle theorem for the other two.
![\bf \measuredangle 1=\cfrac{x-32}{2}\implies \measuredangle 1 =\cfrac{32}{2}\implies \measuredangle 1 = 16 \\\\[-0.35em] ~\dotfill\\\\ \measuredangle 5 =\cfrac{2x}{2}\implies \measuredangle 5 = x\implies \measuredangle 5 = 64 \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cmeasuredangle%201%3D%5Ccfrac%7Bx-32%7D%7B2%7D%5Cimplies%20%5Cmeasuredangle%201%20%3D%5Ccfrac%7B32%7D%7B2%7D%5Cimplies%20%5Cmeasuredangle%201%20%3D%2016%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cmeasuredangle%205%20%3D%5Ccfrac%7B2x%7D%7B2%7D%5Cimplies%20%5Cmeasuredangle%205%20%3D%20x%5Cimplies%20%5Cmeasuredangle%205%20%3D%2064%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\bf \measuredangle 2 = \cfrac{(2x+8)~~-~~(x-32)}{2}\implies \measuredangle 2=\cfrac{2x+8-x+32}{2} \\\\\\ \measuredangle 2=\cfrac{x+40}{2}\implies \measuredangle 2=\cfrac{104}{2}\implies \measuredangle 2=52 \\\\[-0.35em] ~\dotfill\\\\ \measuredangle 6=\cfrac{[(2x+8)+(x)]~~-~~(2x)}{2}\implies \measuredangle 6=\cfrac{3x+8-2x}{2}\implies \measuredangle 6=\cfrac{x+8}{2} \\\\\\ \measuredangle 6=\cfrac{72}{2}\implies \measuredangle 6=36](https://tex.z-dn.net/?f=%5Cbf%20%5Cmeasuredangle%202%20%3D%20%5Ccfrac%7B%282x%2B8%29~~-~~%28x-32%29%7D%7B2%7D%5Cimplies%20%5Cmeasuredangle%202%3D%5Ccfrac%7B2x%2B8-x%2B32%7D%7B2%7D%20%5C%5C%5C%5C%5C%5C%20%5Cmeasuredangle%202%3D%5Ccfrac%7Bx%2B40%7D%7B2%7D%5Cimplies%20%5Cmeasuredangle%202%3D%5Ccfrac%7B104%7D%7B2%7D%5Cimplies%20%5Cmeasuredangle%202%3D52%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cmeasuredangle%206%3D%5Ccfrac%7B%5B%282x%2B8%29%2B%28x%29%5D~~-~~%282x%29%7D%7B2%7D%5Cimplies%20%5Cmeasuredangle%206%3D%5Ccfrac%7B3x%2B8-2x%7D%7B2%7D%5Cimplies%20%5Cmeasuredangle%206%3D%5Ccfrac%7Bx%2B8%7D%7B2%7D%20%5C%5C%5C%5C%5C%5C%20%5Cmeasuredangle%206%3D%5Ccfrac%7B72%7D%7B2%7D%5Cimplies%20%5Cmeasuredangle%206%3D36)
