A rectangular pen with a peimeter of 60 Ft. is needed to house three pigs. Determine an equation to model the area of this pen?
Rectangles have two dimensions: let's call them base (b) and height (h). Perimeter of 60 ft. means that
2b + 2h = 60
Solving for one variable in terms of the other:
2(b+h) = 60
b + h = 30
b = 30 - h
So now we can put this into the area formula: A = bh, giving area of the pen as a function of the length of one side:
A(h) = h(30-h)
Normally you would then be asked which value of h maximizes the area. Can you figure it out?