SOLUTION: A farmer wants in enclose a rectangular plot of land with an area of 600 sq.ft. that borders on a river. The length of the plot needs to be 15 feet shorter than three times the wid

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Question 211385: A farmer wants in enclose a rectangular plot of land with an area of 600 sq.ft. that borders on a river. The length of the plot needs to be 15 feet shorter than three times the width. If you do not fence the side along the river, find the amount of fencing that is needed - to the nearest tenth of a oot. Quadratic equation
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A farmer wants in enclose a rectangular plot of land with an area of 600 sq.ft.that borders on a river.
The length of the plot needs to be 15 feet shorter than three times the width.
If you do not fence the side along the river, find the amount of fencing that is needed - to the nearest tenth of a foot.
Quadratic equation
:
"length of the plot needs to be 15 feet shorter than three times the width."
L = 3W - 15
:
The area given:
L * W = 600
Replace L with (3W-15)
W(3W-15) = 600
3W^2 - 15W = 600
3W^2 - 15W - 600 = 0
Simplify, divide by 3:
W^2 - 5W - 200 = 0
Use the quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this equation x=W; a=1; b=-5; c=-200
W+=+%28-%28-5%29+%2B-+sqrt%28-5%5E2-4%2A1%2A-200+%29%29%2F%282%2A1%29+
W+=+%285+%2B-+sqrt%2825+-+%28-800%29+%29%29%2F2+
W+=+%285+%2B-+sqrt%2825+%2B+800+%29%29%2F2+
W+=+%285+%2B-+sqrt%28825+%29%29%2F2+
The positive solution
W+=+%285+%2B+28.723%29%2F2+
W = 33.732%2F2
W = 16.86 ft is the width
:
Find the length
L = 3(16.86) - 15
L = 50.58 - 15
L = 35.58 ft is the length
:
Find the length of the fence (3 sides)
P = 35.58 + 2(16.86)
P = 35.58 + 33.72
P = 69.3 ft of fence required
:
:
Check solution by finding the area with these values:
35.58 * 16.86 = 599.9 ~ 600 sq/ft