Question

Enclosing a Rectangular Field: Beth has 3000 feet of fencing available to enclose a rectangular field.

(a) Express the area A of the rectangle as a function of x, where x is the length of the rectangle.

(b) For what value of x is the area largest?

(c) What is the maximum area?

Short answer

(a) The area A of the rectangle as a function of length,x of the rectangle is $A=-x^2+1500x$.

(b) The area is largest for $x=750$.

(c) The maximum area is 562,500 square feet.

Step-by-step solution

(a) Step 1. Given information.

Given that Beth has 3000 feet of fencing available to enclose a rectangular field.

(a) Step 2. 

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