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 an area of 169 square feet. Find the width o the deck space around the hot tub, x.Part 1 Write an 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.Part 2Substitute the area of the enclosed space for y in your equation.Part 3 Solve your equation from part 2 for x.Part 4 What is the width of the deck around the hot tub

Question

Answer:

Part 1
The area of a square is:
y = (side length) ^ 2
The length of each side will be given by:
L = 6 + 2x
Substituting we have that the area is:
y = (6 + 2x) ^ 2
Part 2
Substituting the area we have:
y = (6 + 2x) ^ 2
169 = (6 + 2x) ^ 2
Part 3
We solve the equation for x:
root (169) = (6 + 2x)
2x = root (169) -6
x = (root (169) -6) / (2)
x = 3.5 feet
Part 4
The width of the deck around the hot tub is:
3.5 feet

solved

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