# Pre-Calculas 11

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a farmer wants to build two pens (one for cows, the other for horses) on land by a straight road. There is already a fence along the road and the farmer has 800m of fencing to build his fence to enclose the pens and separate them as shown in the diagram below. what is the maximum area of the lot?

• Pre-Calc - incomplete -

• Pre-Calculas 11 -

I cannot see the diagram, so I am going to assume the new fencing is formed into an 'E' shape, with the opening pressed up against the existing fence line. That is: one long side (l), two short sides and the divider (3w).

The fence length is:
800 = 3w + l

So the area is :
A = l w
A = 800 w - 3 w2

The maximum area will be the value of the vertex of this parabola. Find w of this point.

• Pre-Calculas 11 -

There is no diagram given its just what the question says. There is no other info

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