Question

If 400 feet of fencing is used to enclose a rectangular plot of land that borders a river, what is the maximum area that can be enclosed?

Answer 1

It's pretty east to start out.

Use the formulas:
A = w * h
P = 2h + w

where P is the perimeter of the fence (400 ft), h is the length of one of the 2 parallel sides, and w is the length of the side that is parallel to the river.

Answer 2

okay so 400 = 2h + w

now what?

Answer 3

system of equations?

Answer 4

so solve for either h or w in that equation and substitute that into the Area formula

Answer 5

okay so w = 200/h

Answer 6

no quite

Answer 7

so 400 = 2h + 200/h

Answer 8

w = 400 - 2h

Answer 9

argh okay ...

Answer 10

so 400 = 2h + (400 - 2h)

Answer 11

so that w should be substituted into the Area formula:
A = w * h
so
A = (400 - 2h) * h

Answer 12

A = 400 -2h^2

Answer 13

A = 400h - 2h^2

Answer 14

and now just find the derivative and set if equal to 0?

Answer 15

and yes. take the derivative, set to 0, and that will give you h. you can find w from that, which will give you the total area

Answer 16

so then h = 100 right?

Answer 17

indeed it does!

Answer 18

is w just the x coordinate at x =100?

Answer 19

i mean y coordinate?

Answer 20

sure. if you're mapping w (y-coord) against h (x-coord).

Answer 21

okay so then my area would be 15000?