SOLUTION: "The length of a rectangular patio is 8 feet less than twice it's width. The area of the patio is 280 square feet. Find the dimensions of the patio." I know for this problem tha

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Question 962358: "The length of a rectangular patio is 8 feet less than twice it's width. The area of the patio is 280 square feet. Find the dimensions of the patio."
I know for this problem that:
l=2w-8
w=w
However when I try to put the equation together, it doesn't work out at the end. Thanks for the help
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
"The length of a rectangular patio is 8 feet less than twice it's width. The area of the patio is 280 square feet. Find the dimensions of the patio."
I know for this problem that:
length =2w-8
width =w
----
Equation:
length*width = Area
(2w-8)w = 280
2w^2-8w-280 = 0
---
w^2 -4w - 140 = 0
----
(w-14)(w+10) = 0
----
Positive solution::
width = 14 ft
length = 2w-8 = 28-8 = 20 ft
-----------------
Cheers,
Stan H.
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Answer by MathLover1(20849) (Show Source):
You can put this solution on YOUR website!

The length of a rectangular patio is less than twice it's width.
...eq.1
The area of the patio is .
we know that area is
so, ...now substitute from eq.1
.........solve for
.......both sides divide by

.......write as
......group

since we need the width, we can use only positive solution which is

now, go back to eq.1 and calculate
...eq.1

so, the dimensions of the patio are and