Question

The second feature of your one million dollar pool complex is to have a designated kids pool with a concrete pad along one side of the pool; this way parents will have a nice area to lounge in the sun while watching their children swim. You have designated a total area of 5,000 square feet for the kids pool and the concrete pad. Due to the layout of the land/space you have available, you've determined that the length of the rectangular kids pool must be 30 feet greater than the width. The dimensions of the concrete pad are 20 feet by w feet, where w is the unknown width of the pool that aligns with the concrete pad

Answer 1

width of the pool = 50ft²

Area of the concrete pad = 1000ft²

Area of pool = 4000ft²

Explanation:

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Area of the pool and concrete pad = Length × Width

A = LW ..... 1

If you've determined that the length of the rectangular kids pool must be 30 feet greater than the width, then;

L = 30+W ..... 2

Substitute 2 into 1:

A = (30+W)W

A = W²+30W

Given Total area of concrete pad and pool = 5000ft²

Area of concrete pad+area of pool = 5000

(LW)pool + (LW)concrete pad = 5000

(30+W)W + 20W = 5000 (note that the width are the same (for the concrete and the pool)

W²+30W+20W = 5000

W²+50W-5000 = 0

W²+100W-50W-5000 = 0

W(W+100)-50(W+100) = 50

(W+100)(W-50)=0

W-50 = 0 and W+100 = 0

W= 50 and W = -100

Since width cannot be negative, hence the width of the pool that aligns with the concrete pad is 50feet.

Next is get the area of the concrete pad:

Area of concrete pad = 20w

Area of concrete pad = 20(50)

Area of concrete pad = 1000ft²

Get the area of the pool

Area of concrete pad+area of pool = 5000

1000+area of pool = 5000

Area of pool = 5000-1000

Area of pool = 4000ft²