Question

Part II: A square hot tub will be placed in the center of an enclosed area near the pool. Each side of the hot tub measures 6 feet. It will be surrounded by x feet of deck on each side. The enclosed space is also square and has and area of 169 square feet. Find the width of the deck space around the hot tub, x.

Step 1: Write and equation for the area of the enclosed space in the form y = (side length)^2. Hint: Don’t forget to add x to each side of the hot tub.

Step 2: Substitute the area of the enclosed space for y in your equation.

Step 3: Solve your equation from Part b for x.

Step 4: What is the width of the deck around the hot tub? Hint: One if the answers from Part c is not reasonable.

Answer 1

Part 1:

The area of a square is:

`y = (\text{side length}) ^ 2`

The length of each side will be given by:

`L = 6 + 2x`

Substituting we have that the area is:

`\bold{y = (6 + 2x) ^ 2}`

Part 2:

Substituting the area we have:

y = (6 + 2x) ^ 2

`\bold{169 = (6 + 2x) ^ 2}`

Part 3:

We solve the equation for x:

`√(169) = (6 + 2x)`

`2x = √(169) -6`

`x = (√(169) -6) / (2)`

`\bold{x = 3.5 \ feet}`

Part 4:

The width of the deck around the hot tub is:

3.5 feet