SOLUTION: I have been trying to solve this word problem and could use someone's help(note that the chapter is on quadratic equations): A garden area is 30 ft long and 20 ft wide. A path of

Question 108339: I have been trying to solve this word problem and could use someone's help(note that the chapter is on quadratic equations):
A garden area is 30 ft long and 20 ft wide. A path of uniform width
is set around the edge. If the remaining garden area is 400 ft2, what is the width of the path?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A garden area is 30 ft long and 20 ft wide. A path of uniform width
is set around the edge. If the remaining garden area is 400 ft2, what is the width of the path?
--------
Draw the figure of a rectangle surrounding a rectangle
The inner rectangle has area = 400 ft^2
The larger rectangle has area = 30*20 = 600 sq. ft.
-------------
Let the width of the path be "x" ft.
-------------
Then the inner rectangle has dimensions:
width = 30-2x
length = 20-2x
------------------
EQUATION:
(30-2x)(20-2x)=400
(15-x)(10-x) = 100
150-25x+x^2 = 100
x^2-25x+50 = 0
x = [25 +- sqrt(25^2-4*40)]/2
x = [25 +- sqrt(425)]/2
x = [25 +- 5sqrt(17)]/2
Realistic answer:
x = [25-5sqrt(17)]/2
x = 2.1922.. ft.
====================
Cheers,
Stan H.

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