A rectangular dog pen is constructed using a barn wall as one side and 60 meters of fencing for the other three sides. What is the maximum area of the dog pen?

450 m^2

Step-by-step explanation:

let the length be y m (the single side)

let the width be x m

so according to the question

2x + y = 60

or, y = 60 - 2x

now, Area = xy

= x (60-2x)

= - 2x^2 + 60x

d (Area) / dx = - 4x + 60

= 0 for a max of area

-4x + 60 = 0

x = 15

then y = 30

the width has to be 15 m, and the length has to be 30 m for a maximum area of 15 (30) or 450 m^2.