A farmer has 260 meters of clear plastic fencing. He uses all the fencing to create a rectangular holding pen.

a. Taking x as the length of the pen, find an expression for the width of the pen in terms of x.

b. Given that the area of the pen is 4000 square meters, form an equation and solve it to find x, hence the dimensions of the pen.

...help?

Question

A farmer has 260 meters of clear plastic fencing. He uses all the fencing to create a rectangular holding pen.

a. Taking x as the length of the pen, find an expression for the width of the pen in terms of x.

b. Given that the area of the pen is 4000 square meters, form an equation and solve it to find x, hence the dimensions of the pen.

...help?

anonymous · Answer

a. So we know length is x lets call width w. So 2w+2x=260 Isolate width and u get 260-2x=2w. Divide by 2 and you get 130-x=w
b. Using what we have wx is the area. We substitute in w as (130-x) and multiply that by x to get 130-x^2=4000. x^2=-3870. For the purposes of length we make it positive. x=62.21 and width is 130 minus that and it's 67.79

phi · Answer

shouldn't that be x(130-x)= 4000?

anonymous · Answer

oh oops so yeah, 130x-x^2=4000 and x^2-130x+4000=0. Quadratic formula it and you get 80 as length because length is longer than width and width is 50.