A farmer wants to fence a small rectangular yard next to a barn. Fence for side parallel to the barn will cost 55 per foot and the fence for the other two sides will cost 45 per foot. The farmer has a total of 1650 dollars to spend on the project. Find the dimensions for the yard that will have the largest possible area.

55 divided by 45= 1.222222222222    1650 divided by 1.222222= anserw

Step-by-step explanation:

let m = monomial

let t = trinomial

so, m times t = t.

monomial times a trinomial = another trinomial.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4