Question

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 2
Substitute 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

Answer 1

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