Question

i am working with completing the square in parabolas and there's this word problem i just cannot solve..a farmer wants to make a rectangular corral along the side of a large barn and has enough materials for 60m of fencing. Only 3 sides must be fenced, since the barn wall will form a 4th side. What width of rectangle should the farmer use so that the maximum area is enclosed?.. please help!:(

Answer 1

Assume the corral will not be as long as the barn, and that is goes a distance x away from the barn. There are thus 2 sides with length x and one side with length 60-x. the total area enlosed is
A = x(60-2x)
Choose the value of x that maximizes A by completing the square.
A = -2x^2 + 60 x
= -2(x^2 -30x + 225) + 225
= ??? You finish it. That is a perfect square within the ()