MATH SOLVE

4 months ago

Q:
# 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

Accepted Solution

A:

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

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