SOLUTION: Factoring: 1. A farmer has 300 ft of fencing and wants to enclose a rectangular area of 5000 ft2. What dimensions should she use? (Hint: 5000 = 30 * 100) A=5000 W=? L=? H=? A=

Question 412716: Factoring:
1. A farmer has 300 ft of fencing and wants to enclose a rectangular area of 5000 ft2. What dimensions should she use? (Hint: 5000 = 30 * 100)
A=5000 W=? L=? H=?
A= W*L*H
I know that we're supposed to put all of the numbers to one side and equal them to zero. Ex: 2(x+1)=0 ==> x=-1
Answer by checkley79(3341) (Show Source): You can put this solution on YOUR website!
For a rectangle you only need the Length & the Width measurements.
Thus:
L+W=300
L=300-W
Area=L*W
5,000=(300-W)W
5,000=300W-W^2
W^2-300W+5,000=0

W=(300+-sqrt[-300^2-4*1*5,000])/2*1
W=(300+-sqrt[90,000-20,000])/2
W=(300+-sqrt70,000)/2
W=(300+-265.575)/2
W=(300+262.575)/2
W=564.575/2
W=282.29 ans. for the width.
L=300-282.29=17.71 ans. for the length.
Proof:
5,000=282.29*17.71
5,000=5,000
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