Question 228650: you would like to fence in an area next to your house in which your new puppy will be able to play. you have 10 yards of fencing material to use and plan to use as one side of the play area. (in other words, the ten yards of fencing will only be used for three sides of the play area.) what dimensions should you use in order to maximize the area of the "play pen"? what area will the pen have?
plz help me!!!!
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! you would like to fence in an area next to your house in which your new puppy will be able to play. you have 10 yards of fencing material to use and plan to use as one side of the play area. (in other words, the ten yards of fencing will only be used for three sides of the play area.) what dimensions should you use in order to maximize the area of the "play pen"? what area will the pen have?
.
Let x = width of play area
then
10-2x = length of play area
.
Area = x(10-2x)
Area = -2x^2+ 10x
This is a parabola that opens downward. In other words, if we find the vertex, it will be the maximum.
x = -b/2a is the "axis of symmetry"
x = -10/2(-2) = -10/-4 = 5/2 yards (width)
.
Length:
10-2x = 10-2(5/2) = 10-5 = 5 yards (length)
.
Our dimensions of play area:
5/2 by 5 yards
.
Our area:
5/2 * 5 = 25/2 square yards = 12.5 square yards
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