Answer:
Length: 16 feet
Width: 25 feet
Explanation:
Alright so let's set up our system:
The area of a rectangular patio is 400 square feet.: L*W = 400
The length of the patio is 9 feet more than its width: L = W - 9
If you look here, all we need to do now is plug in L and solve.
(W - 9)W = 400
W^2-9W - 400 = 0
You can attempt to factor this in a number of ways. I recommend a factor tree, but however you do that is fine.
(W + 16)(W - 25) = 0
so we have two W values now, 25 and -16. Which one do we pick? We pick 25, because we cannot have a negative Width. That would literally break the universe.
So now we plug in 25 in our second equation to get L:
L = 25 - 9
L = 16
And now we have both our answers!