SOLUTION: A rectangle yard with an area of 50 m squared is to be fenced on three sides. minimizing the perimeter will minimize the cost of the fence. conduct an investigation to determine th

Algebra ->  Rectangles -> SOLUTION: A rectangle yard with an area of 50 m squared is to be fenced on three sides. minimizing the perimeter will minimize the cost of the fence. conduct an investigation to determine th      Log On


   

Question 872732: A rectangle yard with an area of 50 m squared is to be fenced on three sides. minimizing the perimeter will minimize the cost of the fence. conduct an investigation to determine the shape of the yard with minimum perimeter.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Wanting the minimum perimeter,
dimensions x and y
xy=50 and p=2x+2y;
y=50%2Fx, so substituting, p=2x%2B2%2850%2Fx%29, and we have no way to distinguish between x and y.
highlight%28p=2x%2B100%2Fx%29.
p=%282x%5E2%2B100%29%2Fx, the minimum seems to occur near x=7, using a graphing program.

Also, using derivative of p with x,
2-100%2Ax%5E%28-2%29=0
2=100%2Fx%5E2
x%5E2%2F100=1%2F2
x%5E2=100%2F2
x=sqrt%2850%29
x=sqrt%282%2A5%2A5%29
highlight%28x=5sqrt%282%29%29, which is approx. 7.07107
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The y value would be 50%2F%285sqrt%282%29%29=10%2Fsqrt%282%29=10sqrt%282%29%2F2=highlight%285sqrt%282%29%29, which is the same value as x.