SOLUTION: A 10m by 34m garden is surrounded by a walkway of uniform width (call it "x"). The total area of the garden and walkway is 640 square meters. what is the width of the walkway?
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Question 165093: A 10m by 34m garden is surrounded by a walkway of uniform width (call it "x"). The total area of the garden and walkway is 640 square meters. what is the width of the walkway?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x = width of the path
With these type of problems, it helps to draw a picture. So draw two rectangles, one inside of the other, and label the inside rectangle's dimensions:
Now the label the width of the path "x" (denoted in red)
Since there are 2 "x" lengths per side, this means that you need to add "2x" to both the length and width of the inner rectangle to get the length and width of the outer rectangle. If this makes no sense at all, here's a visual:
So the length and width of the outer rectangle is and respectively. This means that for the outer rectangle (the given area of both the walkway and the garden), and
Remember, the area of any rectangle is
Start with the area of a rectangle formula
Plug in , and
FOIL
Subtract 640 from both sides.
Combine like terms.
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 possible answers are or
However, since a negative width is not possible, this means that is NOT a solution.
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Answer:
So the solution is which means that the width of the path is 3 meters.
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