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put this solution on YOUR website!The length of a pool is 3 times its width, and the pool is surrounded by a grass walk 4 feet wide. If the total area enclosed by the walk (of uniform width) is 684 square feet, find the dimensions of the pool.
This is quadratic equation word problem using a geometric figure...our swimming pool.
Information Given:
width = x...x is the unknown.
length = 3 times x or 3x.
Area = 684ft^2...We use a square because area is measured in SQUARE UNITS.
Grass walk = 4 feet wide
We know that if the grass walk surrounds the pool, it must be 4 feet wide all AROUND the pool. Make sense?
Here is the equation:
(3x + 8) times (x + 8) = 684
We use the FOIL method on the left side to get:
3x^2 + 24x + 8x + 64, which then becomes:
3x^2 + 32x + 64
We equate 3x^2 + 32x + 64 to the given area and we get:
3x^2 + 32x + 64 = 684
Subtract 684 from BOTH sides and we are left with:
3x^2 + 32x + 64 - 684 = 0
3x^2 + 32x -620 = 0
Factor the left side using groups.
3x^2 + 62x - 30x - 620 = 0
(3x^2 + 62x) = Group A
(- 30x - 620) = Group B
Factor each group separately.
Group A becomes x(3x + 62).
Group B becomes -10(3x + 32)
We now have this equation:
(x - 10)(3x + 62) = 0
Set each factor to 0 and solve for x.
x - 10 = 0
x = 10
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3x + 62 = 0
3x = -62
x = -62/3....This value for x is REJECTED because we are looking for the dimensions of the pool. Dimensions are distances and DISTANCE CANNOT be negative. Is this clear?
We use x = 10 to find our dimensions.
As I said above:
width = x
length = 3 times x or 3x
I just found that x = 10, right?
Then our width is 10 feet and the length is 3x = 3(10) = 30 feet.
Width = 10 feet
Length = 30 feet
Got it?
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