What is x? What is the greatest common factor? Please help asap

Question

The Adult Pool Area has a total area of 15,000 square feet. The Adult

Pool Area consists of a rectangular swimming pool and a concrete

walkway of even width surrounding all four sides of the pool. The

swimming pool is 120 ft. by 70 ft.

○ Hint: First draw a picture of the pool and the walkway surrounding

it on all four sides and label the walkway of even width, x.

● Now label your picture with an expression for the total length, including

the walkway. Then label your picture with an expression for the total

width, including the walkway.

○ Hint: There are two widths of the walkway for both the total length

and width.

● Using the expressions for total length and width, find an expression for the total area of the

rectangular pool and walkway. In order to solve for x, you will need to set the expression for area

equal to the 15,000 square feet. Now use your factoring skills to solve.

○A = l · w

○ Set your equation equal to zero (subtract the 15,000 on both sides).

○ Is there a Greater Common Factor?

● Now that you have found the width of the concrete walkway surrounding the pool, you should be

able to sketch out a quick drawing of the Adult Pool Area with all dimensions labeled. This drawing

will help you keep your measurements straight as you continue with the project.

Answer 1

So, draw your picture of a swimming pool with a length of 120 ft and a width of 70 ft. Draw a "frame" around it, remembering that that it sticks out x from the top, bottom, left, and right.

That gives us...

15,000 = (120 + 2x)(70 + 2x)

You'd think you'd just add x to each, but again, if you were to walk the width of the pool area, you'd go x feet, 70 feet along the pool, and another x feet to the end of the concrete. Same with the length, x feet, 120 feet, and another x feet.

15,000 = 8400 + 380x + 4x²

4x² + 380x - 6600 = 0

4(x² + 95x - 1650) = 0

x² + 95x - 1650 = 0

(x + 110)(x - 15) = 0

x + 110 = 0

x = -110

Well, we can't have a negative length, so this solution is out.

x - 15 = 0

x = 15 feet

The concrete walkway is 15 feet wide.