Question

x^2+y=120
find y.
what is the max area?

(the problem is this: a rectangle and a fence to cover 3 sides, find area of the longest side.)

Answer 1

Is the Perimeter = 120?

Answer 2

WELL THE FENCING NEED FOR 3 SIDES IS 120

Answer 3

o.k. then 2x + y = 120 because two of the sides are the same, 2x, and the other side doesn't have to be, y.
so using this equation you get y = 120 - 2x
Area = Length * Width = y * x = (120 - 2x)*x
That is
A = 120x - 2x^2 or prettier:
\[A = 120x -2x^2\]
This is an upside down parabola so the maximum will be at the vertex.
When you find the x value of the vertex, plug it into the equation \[A = 120x -2x^2\] to get the maximum area
Does that help?