SOLUTION: Lora Wallman wishes to fence in a rectangular region along a river bank with only 3 sides. If she has only 400 feet of fencing and wishes to enclose an area of 15,000 sq feet, fin

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Lora Wallman wishes to fence in a rectangular region along a river bank with only 3 sides. If she has only 400 feet of fencing and wishes to enclose an area of 15,000 sq feet, fin      Log On


   

Question 960228: Lora Wallman wishes to fence in a rectangular region along a river bank with only 3 sides. If she has only 400 feet of fencing and wishes to enclose an area of 15,000 sq feet, find the dimensions of the rectangular region.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let the regions dimensions be L and W.
The area of the region is,
L%2AW=15000
and the amount of fencing used is,
W%2BL%2BW=400
2W%2BL=400
L=400-2W
Substituting,
%28400-2W%29W=15000
-2W%5E2%2B400W=15000
W%5E2-200W%2B7500=0
%28W-50%29%28W-150%29=0
Two solutions:
W-50=0
W=50
Then,
L=400-2%2850%29
L=400-100
L=300
50Wx300L
and
W-150=0
W=150
Then,
L=400-2%28150%29
L=400-300
L=100
150Wx100L