SOLUTION: Mike has 400 yards of net and wants to enclose a rectangular area. 1. Express area of A as a function of the width (w). 400=2(w+1) ??????? 2. For what value of w is the area

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Mike has 400 yards of net and wants to enclose a rectangular area. 1. Express area of A as a function of the width (w). 400=2(w+1) ??????? 2. For what value of w is the area       Log On


   

Question 1009099: Mike has 400 yards of net and wants to enclose a rectangular area.
1. Express area of A as a function of the width (w).
400=2(w+1)
???????
2. For what value of w is the area the largest?
?????????
3. What is the maximum area?
????????
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
w and L, the dimensions, and perimeter is 2w%2B2L=400. Simplify this!
w%2BL=200.

Area is wL, and naming area as a function, you may choose A.
A=wL.

You want to be more specific for which is the input variable for A. Look at the simplified perimeter equation.
Either w=200-L or L=200-w. Choose one and work with it.

One way, A as a function of w;
highlight%28A%28w%29=w%28200-w%29%29;
and using this in this factored form will be convenient. This A(w) is a parabola with vertex as a maximum point. The vertex occurs in the exact middle of the roots or zeros, using w as the horizontal axis values.