SOLUTION: You want to fence in a rectangular plot with an area of exactly 360 square meters. 1. Using diagrams, functions, and graphs, determine the possible dimensions if you can use at

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: You want to fence in a rectangular plot with an area of exactly 360 square meters. 1. Using diagrams, functions, and graphs, determine the possible dimensions if you can use at       Log On


   

Question 918408: You want to fence in a rectangular plot with an area of exactly 360 square meters.
1. Using diagrams, functions, and graphs, determine the possible dimensions if you can use at most 100 meters of fence.
2. Determine the dimensions of the plot with the shortest perimeter.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
xy=360, and perimeter p=2x+2y.

y=360%2Fx;
substituting,
p=2x%2B2%28360%2Fx%29
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QUESTION 1:
p%3C=100.
highlight_green%282x%2B2%28360%2Fx%29%3C=100%29
x%2B360%2Fx%3C=50
x%5E2%2B360%3C=50x, you can expect x to be POSITIVE.
highlight_green%28x%5E2-50x%2B360%3C=0%29----finally we analzye according to a function based on this equation.

Discriminant: 50^2-4*360=1060,
sqrt(1060)=stillIrrational;
1060=106*10=53*2*2*5
sqrt(1060)=2sqrt(5*53)=2sqrt(265)

highlight_green%28highlight%28x=%2850%2B-+2sqrt%28265%29%29%2F2%29%29
The way the variables occur in the formulas, one of these forms maybe work for x and the other form will work for y; the two dimensions....
x and y must be BETWEEN the two roots found for "x".
That is because the inequality is based on a parabola with a minimum vertex.

y=x^2-50x+360
graph%28300%2C300%2C-10%2C70%2C-10%2C110%2Cy=x%5E2-50x%2B360%29