A man built a walk of uniform width around a rectangular pool. If the area of the walk is 429 square feet and the dimensions of the pool are 10 feet by 18 feet, how wide is the walk?
area of walk of width w plus pool
(10+2w)(18+2w) = 180+429 = 609
4w^2 + 56w + 180 = 609
(2w-11)(2w+39) = 0
e = 11/2
To find the width of the walk, we can start by calculating the total area of the rectangular pool and the walk combined.
The area of the rectangular pool is given by the length multiplied by the width, which is 10 ft * 18 ft = 180 square feet.
Let's denote the width of the walk as "w."
The dimensions of the entire area, including the rectangular pool and the walk, can be represented as follows:
Length: 10 feet + 2w (there are two sides of the walk)
Width: 18 feet + 2w (there are two sides of the walk)
The area of the entire area is given by the length multiplied by the width:
(10 + 2w) * (18 + 2w) = 429 square feet
Now, we can solve this equation to find the value of "w."
Start by expanding the equation:
180 + 20w + 18w + 4w^2 = 429
Combine like terms:
4w^2 + 38w + 180 = 429
Subtract 429 from both sides to set the equation equal to zero:
4w^2 + 38w + 180 - 429 = 0
Combine like terms:
4w^2 + 38w - 249 = 0
Now, we can solve this quadratic equation. You can use factoring, completing the square, or the quadratic formula to find the value of "w."