I just need help setting up the equation - the rest I can do on my own: A man built a walk of uniform width around a rectangular pool. If the area of the walk is 253 square feet and the dimensions of the pool are 9 feet by 3 feet, how wide is the walk?
pool area = 9 * 3 = 27
total area = 27 + 253 = 280
so (2w + 9) * (2w + 3) = 280
4w^2 + 6w + 18w + 27 = 280
Thank you!
glad to help
To solve the problem, we need to set up an equation that relates the dimensions of the pool and the walkway.
Let's start with the dimensions of the walkway. We don't know the width of the walkway, so let's call it 'x' feet.
Now, let's consider the overall dimensions of the area occupied by the walkway and the pool combined. To find the length and width of this area, we add twice the width of the walkway to the dimensions of the pool. Thus, the length becomes 9 + 2x feet, and the width becomes 3 + 2x feet.
The area of the walkway is given as 253 square feet. The area of the overall space (including the pool and the walkway) will be the length multiplied by the width. So, the equation becomes:
(9 + 2x) * (3 + 2x) = 253
Now, you can solve this quadratic equation for 'x' to find the width of the walkway.