A(w)=50w-w2 if the perimeter is 100, I plugged in possible values for the width...I used w=15 and length = 35 for a perimeter of 100. then I plugged these values in the possible equations until I found the correct one giving me an area of 525 (15x35) . I could not think of an easier way.
Answer:
[tex]A(w)=50w-w^2[/tex]
Step-by-step explanation:
Let w be the width of rectangular pen.
We have been given that a framer has 100 m of fencing to enclose a rectangular pen. This means that perimeter of pen is 100 meter.
Since the perimeter is 2 times the length and width of rectangle.
[tex]\text{Perimeter of rectangle}=2\text{ (Width+Length})[/tex]
Upon substituting our given values in above formula we will get,
[tex]100=2(w\text{+Length})[/tex]
[tex]\frac{100}{2}=\frac{2(w\text{+Length})}{2}[/tex]
[tex]50=w\text{+Length}[/tex]
[tex]50-w=w-w\text{+Length}[/tex]
[tex]50-w=\text{Length}[/tex]
[tex]\text{Area of rectangle}=\text{Width*Length}[/tex]
Upon substituting our given values in area formula we will get,
[tex]\text{Area of rectangle}=w(50-w)[/tex]
[tex]\text{Area of rectangle}=50w-w^2[/tex]
Let us represent area in terms of width of rectangle as:
[tex]A(w)=50w-w^2[/tex]
Therefore, the area of our given pen will be [tex]A(w)=50w-w^2[/tex].
