Question

Q7: A farmer wants to build a metal fence to enclose his livestock. The fence's vertices are represented by

points A(4,-4), B(-4,-4), C(-4, 3), D(1, 3), E(1,-1), and F(4,-1). Each unit in the coordinate plane
represents 1 meter in reality. Since a gate is to be added between points A and F. the farmer will not use
metal fencing on that side. What is the total number of meters of metal fencing the farmer needs?

Answer 1

Answer:down below

Step-by-step explanation:A square gives the greatest area. If the river were not there, you would divide 1700 by 4 to get a square 425 feet by 425 feet. Because of the river, add 425 feet to the side opposite the river to get a rectangle 425 feet by 850 feet.

Now for the algebra that you need.

P=2l+2w but there is only one length.

P=l+2w

1700=l+2w

1700-2w=l

A=lw

A=(1700-2w)w

A=1700w-2w2

This is a parabola that opens downward so there is a maximum point, the vertex, which is (h,k).

h=-b/2a is the "maximizing point" and k is the maximum area

-b/2a=-1700/(-4)

-b/2a=425 feet

One width will be 425 feet, the length will be (425+425)=850 feet, and the second width will also be 425 feet.

A=lw

The maximum area will be A=850*425=361,250 square feet.

Notice that if you substitute 425 into the equation A=1700w-2w2 you will get the same answer.

1700*425-2*4252

722,500-2*180,625

722,500-361,250