Question

To make an enclosure for chickens, a rectangular area will be fenced next to a house. Only three sides will need to be fenced. There is 120 ft of fencing material. What quadratic function represents the area of the rectangular enclosure, where x is the distance from the house? What dimensions will maximize the area of the enclosure?

Answer 1

Answer:

Let the length parallel to the house be y

let each of the other two equal sides be x

2x + y = 120

y = 120 - 2x

Area = xy

= x(120 - 2x) or -2x^2 + 120x

b) you want the vertex.

x of the vertex is -120/(-4) = 30

when x = 30

y = 60

Maximum area = xy = 1800 ft^2