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?

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nathanshields | High School Teacher | (Level 1) Associate Educator

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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?