To make an enclosure for chickens, a rectangular area will be fenced next to a house. Only 3 sides will need to be fenced. There is 120 ft. of fencing material.

Question

To make an enclosure for chickens, a rectangular area will be fenced next to a house. Only 3 sides will need to be fenced. There is 120 ft. of fencing material.
a. What quadratic function represents the area of the rectangular enclosure, where x is the distance from the house?

b. what dimensions will maximize the area of the enclosure?

Reiny · Accepted 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

Anonymous · Answer

Roller coaster that has uphill climb of 255 feet at an angle of 38 degrees on its largest hill

Just k · Answer

a. -2x²+120x b. max area= 1800ft²