SOLUTION: Two gardeners are building fences around each of their rectangular 100 square yard gardens. One gardener purchases 62 yards of fencing. The other purchases 30 yards of fencing. Ex

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Question 876438: Two gardeners are building fences around each of their rectangular 100 square yard gardens. One gardener purchases 62 yards of fencing. The other purchases 30 yards of fencing. Explain the reason for each gardener purchasing different lengths of fencing even though both gardens are 100 yards in area.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The dimensions of each garden can be solved. The length and width of one garden are different than the length and width of the other garden.

You can go forward with these two gardens using these relationships:
x and y are dimensions.
Constants: A for area, p for perimeter
Unknowns: x and y either for length and width
xy=A and 2x+2y=p.
2y=p-2x,
highlight%28y=%28p-2x%29%2F2%29;
x%28p-2x%29%2F2=A
x%28p-2x%29=A
px-2x%5E2=A
-2x%5E2%2Bpx-A=0
highlight%282x%5E2-px%2BA=0%29
Use and solve the quadratic equation first and then use the value in the linear equation for y.