Question

A rancher is building a rectangular corral. He is using one wall of his barn as one of the sides. The barn wall is long enough that the rancher only needs to create the other three sides. The rancher has 400 ft of fencing total. Find the maximum area of the corral and the dimensions that make that happen. a) length of the corral: feet b) width of the corral: feet c) maximum area of the corral: sq feet d) Write a formula to represent the area of the corral using x as the length: e) Use your answer to question d to justify your anwer to questions a-c. Write a summary of your reasoning.

Answer 1

Answer:

A = the total area of the two corrals x = the length of the non-adjacent sides of each corral

Function to maximize: A = 2x × 400 - 4x

3

where 0 < x < 100

Dimensions of each corall: 50 ft (non-adjecent sides) by

200

3

ft (adjacent sides)

Hope this helps