SOLUTION: If you have 30 feet of wood to build the border of a flower garden. If you want to build a rectangle with the largest area possible to plant flowers, what would the area be? Prove

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Question 1076116: If you have 30 feet of wood to build the border of a flower garden. If you want to build a rectangle with the largest area possible to plant flowers, what would the area be? Prove your answer using words and or numbers. Use only whole numbers.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Dimensions x and y.

Perimeter: 2%28x%2By%29=30
x%2By=15
y=15-x

Area: xy
x%2815-x%29
Variable A for area, A%28x%29=x%2815-x%29
A can take the form of a parabola if graphed.
A(x)=x(15-x) has when multiplied, an -x%5E2 term so the parabola has a maximum point exactly in the middle of the Zeros of A.

x%2815-x%29=0
system%28x=0%2Cor%2Cx=15%29

The maximum area will be x=%2815%2B0%29%2F2=7%261%2F2

Now find y.
y=7%261%2F2


Both x and y are each 7%261%2F2.
This is a square shape.

A%287.5%29=%287.5%29%5E2
A%287.5%29=highlight%2856%261%2F4%29