Determine dimensions of rectangle that will make area maximum

Question

a rectan pen is to be made with 120 m fencing pen is divided into 4 parts and and exist propert fence will be used for one lomg side

if x represents width of fence express area A(x) in terms of x and 

 

Determine dimensions of rectangle that will make area maximum

Answer 1

If the pen has 4 parts, there will be 5 pieces of fence that are width x.

 

The length will be 120 - 5x.

 

A(x) = x(120 - 5x) or 600x - 5x²

 

a = -5, b = 600. 

 

Use h = -b/(2a) to get x, then max area will be A(h).