help pleaseeeeeeee!

Question

A cowgirl is going to fence in a rectangular area to keep her horses. One side of her property borden the rectangular pasture.which already has a fence. therefore, she will only need to put 10 fence on three sides of her property. she only has enough supplies to build 240m of fence. determine the dimension of the largest possible rectangular lot in term of its area. Diagram and label

Answer 1

Let x be the length of fence opposite the neighbor's fence. and let y be the length of each of the other two sides.

Then the total fence is 240m.

Therefore x + 2y = 240

Re-write the equation y = (240 - x)/2

Now Area of the fence is A = xy.

Then A = x((240 - x)/2)

Now for the largest rectangular in terms of area, we make dA/dx = 0.

Now dA/dx = 0

240 - 2x = 0

x = 120.

If x=120 the y = (240-x)/2 = 60.

Therefore x = 120 and y = 60.