Question

Please help!
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

The area of the enclosed space is given by the equation
(6+2x)² = 169

We can take the square root of both sides, since 169 is a perfect square:
√(6+2x)² = √169
6 + 2x = 13

Subtract 6 from each side:
6 + 2x - 6 = 13 - 6
2x = 7

Divide both sides by 2:
2x/2 = 7/2
x = 3.5