MATH SOLVE

3 months ago

Q:
# 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 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:

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

(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