A rectangular area is to be enclosed by a wall on one side and fencing on the other three sides. If 18 meters of fencing is are used, what is the maximum area that can be enclosed?

Question

A: 9/2 m^2

B:81/4 m^2

C: 27 m^2

D: 40 m ^2

E: 81/2 m^2

Answer 1

Assign variables: X is the length of the side opposite the wall, Y is the length of the other 2 sides.

We are given X + 2Y = 18 meters, so X = 18 - 2Y (equation 1)

The area is A = X * Y

Replace X using equation 1:

A(Y) = (18 - 2Y) * Y

A(Y) = -2Y² + 18Y

To find the maximum area, take the derivative, dA/dY, and set equal to zero, and solve for Y. Then solve A(Y) to find A.