SOLUTION: The Smith's have 160 meters of fencing available to build a rectangular garden. One side of the garden touches a side of the house and doesn't need any bordering. Algebraically fin

Question 177927: The Smith's have 160 meters of fencing available to build a rectangular garden. One side of the garden touches a side of the house and doesn't need any bordering. Algebraically find the dimensions that will give the maximum area.
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
One side of the rectangle is taken up by the house.
That leaves 3 sides taken up by fencing.
Let's call that side W for width and the other two sides will be L to use up the fencing.
1.
The area of the rectangle will be
2.
Use eq. 1 and make the area a function of only one variable.
1.

Now we can differentiate with respect to L and set the derivative equal to zero.

Let's plot the graph of area as a function of length to make sure the area is maximum at this point,

From eq. 1,

The area is then,

Width of 80 m, length of 40 m, yields a garden of 3200 sq. meters.
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