can u please help me with this math problem. i don't get how to do this question.
Mrs. Mabie has a rectangle swimming pool that measures 25 feet by 14 feet. She wants to have a cement walkway installed around the perimeter of the pool. The combined area of the pool and walkway will be 672 square feet. What will be the width of the walkway?
let the width of the walkway be x ft
dimensions of the whole thing = (25+2x) by (14+2x)
(25+2x)(14+2x) = 672
350 + 78x + 4x^2 - 672=0
4x^2 + 78x - 322 = 0
x = (-78 ± √11236)/8
= 3.5 or a negative
the width should be 3.5 ft
check:
length = 25+7 = 32
width = 14 + 7 = 21
32 x 21 = 672
Of course, I'd be happy to help you with this math problem!
To find the width of the walkway, we'll need to subtract the area of the pool from the combined area of the pool and walkway. Here's how you can do it step-by-step:
1. Start by calculating the area of the pool. The formula to find the area of a rectangle is length x width. In this case, the length is 25 feet and the width is 14 feet. So, the area of the pool is 25 feet x 14 feet = 350 square feet.
2. Next, subtract the area of the pool from the combined area of the pool and walkway to find the area of the walkway. In this case, the combined area is given as 672 square feet. So, the area of the walkway is 672 square feet - 350 square feet = 322 square feet.
3. Now, since we know the length and width of the pool, but not the dimensions of the walkway, we'll need to use a variable to represent the width of the walkway. Let's call it "x".
4. To find the dimensions of the walkway, we'll need to set up an equation. The area of the walkway is calculated by multiplying the length (25 feet + 2x) by the width (14 feet + 2x). So, we have the equation (25 + 2x)(14 + 2x) = 322.
5. Now, we can solve this equation to find the value of x. Simplifying the equation, we get (25 + 2x)(14 + 2x) = 322. Expanding and rearranging, we have 4x^2 + 78x - 18 = 0.
6. To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, factoring might not be simple, so using the quadratic formula is a better option.
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the value of x is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 4, b = 78, and c = -18.
7. Substitute these values into the quadratic formula and calculate to find the two possible values of x.
Once you have calculated the values of x, check if they make sense in the context of the problem. Since we are looking for the width of the walkway, the value of x should be positive and reasonable.
So following these steps, you can find the width of the walkway around Mrs. Mabie's pool.