We need to use what we know about rectangles to get:
1)
- Total length = 2*W + 8ft
- Total width = W + 8ft
2) area = 2*W^2 + 24ft*W + 64ft^2
Working with rectangles:
We know that rectangles are defined by two measures, width W and length L.
Here we do know that the length of the pool is twice the width, and the width is W, then the length of the pool is:
L = 2*W
And we also have a sidewalk of 4ft all around the pool, now we want to get:
1) The total length and the total width.
This will be equal to the length/width of the pool plus twice the width of the sidewalk (we add it twice because is in both ends) then we have:
- Total length = L + 2*4ft = 2*W + 8ft
- Total width = W + 2*4ft = W + 8ft
2) Now we want to get an expression for the total area of the pool.
Remember that for a rectangle the area is just the product between the width and the length, so to get the area of the pool with the sidewalk we just take:
area = (total length)*(total width)
area = (2*W + 8ft)*(W + 8ft) = 2*W^2 + 3*W*8ft + 64ft^2
area = 2*W^2 + 24ft*W + 64ft^2
This is the equation that gives the total area as a function of W, the width of the pool.
If you want to learn more about rectangles, you can read:
https://brainly.com/question/17297081
