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Let x = width of path
First let's find the area of the garden only: Area of Garden = 18*13=234
So the area of the garden only is 234 square feet.
Now let's draw a picture:
From the picture, notice that the length of the entire rectangle (including the width of the path) is
(notice there are two "x" lengths per side) and the total width is
.
So the area of the entire enclosure (including the path) is the expression
Now subtract off the area of the garden (we only want the area of the path)
FOIL
Combine like terms
So the area of the path only is
Start with the area of the path
Plug in
(which is the area of the path)
Subtract 516 from both sides
Notice we have a quadratic equation in the form of
where
,
, and
Let's use the quadratic formula to solve for x
Start with the quadratic formula
Plug in
,
, and
Square
to get
.
Multiply
to get
Rewrite
as
Add
to
to get
Multiply
and
to get
.
Take the square root of
to get
.
or
Break up the expression.
or
Combine like terms.
or
Simplify.
So the answers are
or
Since a negative width doesn't make sense, this means that the only solution is
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Answer:
So the width of the path can be up to 6 feet (ie 6 feet is the maximum width)
