SOLUTION: A farmer wants to enclose a rectangular lot using 50 meters of fencing materials. If he needs an area of at least 50 SQUARE meters, find the range for the possible length of the lo

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Question 891964: A farmer wants to enclose a rectangular lot using 50 meters of fencing materials. If he needs an area of at least 50 SQUARE meters, find the range for the possible length of the lot.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
w for width and L for length;
2w%2B2L=50 and wL%3E=50.

Using first the perimeter equation, w+L=25
w=25-L
Substitute.
%2825-L%29L%3E=50
25L-L%5E2%3E=50
-L%5E2%2B25L-50%3E=0
highlight_green%28L%5E2-25L%2B50%3C=0%29

roots for the equation
L=%2825%2B-+sqrt%2825%5E2-4%2A50%29%29%2F2
L=%2825%2B-+sqrt%28425%29%29%2F2
L=%2825%2B-+5%2Asqrt%2817%29%29%2F2

The parabola with L has a minimum based on coefficient on L%5E2 being a positive 1. This means that L cannot be between the two roots. The inequality is satisfied for highlight%280%3CL%3C=%2825-5sqrt%2817%29%29%2F2%29 or for highlight%28%2825%2B5sqrt%2817%29%29%2F2%3C=L%3C50%29.