a rectangle of perimeter 100 units has the dimensions shown. Its area is given by the function A = w(50 - w). What is the GREATEST area such a rectangle can have?

Question

jonnyvonny · Answer

We know the formula for the perimeter of a rectangle: P=2l+2w.
We're given the width, so lets get width alone:$$200=2l+2w \rightarrow 100=l+w \rightarrow 100-l=w$$
substitute this equation with the one given: A=w(50-w):
$$100-l=w \rightarrow A=w(50-w)\rightarrow A=(100-l)(50-(100-l))$$$$A=(100-l)(50-100+l)\rightarrow A=(100-l)(-50+l)$$$$A=(100-l)(-50+l)\rightarrow A=-5000+100l+50l+l^2$$$$A=-5000+150l+l^2$$
From there, either factor or get 2 binomials, then cross out that gives a negative x-value. ie. x=-200 or something.

anonymous · Answer

Do you still need help, if not you should close the question.

jonnyvonny · Answer

^