SOLUTION: Please help me answer this question. This is a worksheet. I have consulted my textbook and the resource books my mom bought. I'm very confused. A rancher who raises ostriches

Click here to see ALL problems on Functions

Question 79114: Please help me answer this question. This is a worksheet. I have consulted my textbook and the resource books my mom bought. I'm very confused.
A rancher who raises ostriches has 60 yards of fencing to enclose 4, equally sized, rectangular pens for his flock of ostriches. He is considering two options:
A. Arrange the smaller pens in a line with adjacent pens sharing one common fence. (The diagram shows a rectagle divided vertically into 4 sections.)
B. Arrange the four smaller pens so that they share exactly two common fences as shown in the diagram. (The diagram shows a rectangle that is divided in half horizontally and then vertically.)
The problems is: Define the functions for the total area of each of the two options.
I've tried dividing out 60 and plugging it into each diagram hoping that would help me come up with a function. I also tried working with a linear equation, but I think it suppose to be a quadratic function. I appreciate any help you can give me. Thank you.
Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
you need to define the dimensions of the rectangles in terms of length (l) and width (w) and 60 yards of fence

A. in this case, 2 lines of fence correspond to the length and 5 lines to the width ... so 2l+5w=60 ... or l=(60-5w)/2

since area equals l times w, substituting for l gives ... a=((60-5w)/2)*w ... area =

B. similar to A, 3 lines are equal to the length and 3 lines are equal to the width ... so 3l+3w=60 ... or l=20-w

again, substituting gives ... a=(20-w)*w ... area =

you could also solve for w in terms of l and substitute to get the areas in terms of l