Question

you are designing a rectangular swimming pool inside a backyard that measures 50 feet by 30 feet. you want to include a deck around the pool that is 4 feet wide. what is the maximum possible area for the pool itself?
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the maximum possible length of the pool is □ feet.
the maximum possible width of the pool is □ feet.
therefore, the maximum possible area of the pool is □ square feet.

Explanation:

Step1: Calculate the maximum possible length of the pool

The backyard length is 50 feet. Since the deck is 4 - feet wide on both sides of the pool, we subtract \(2\times4\) from the backyard length.
\(l = 50-2\times4=50 - 8=42\)

Step2: Calculate the maximum possible width of the pool

The backyard width is 30 feet. Since the deck is 4 - feet wide on both sides of the pool, we subtract \(2\times4\) from the backyard width.
\(w=30 - 2\times4=30-8 = 22\)

Step3: Calculate the area of the pool

The area of a rectangle is \(A=l\times w\). Substitute \(l = 42\) and \(w = 22\) into the formula.
\(A=42\times22=(40 + 2)\times22=40\times22+2\times22=880+44 = 924\)

Answer:

The maximum possible length of the pool is \(42\) feet.
The maximum possible width of the pool is \(22\) feet.
Therefore, the maximum possible area of the pool is \(924\) square feet.