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Having trouble with this math word problem.?
Beth has 2700 feet of fencing available to enclose a rectangular field. One side of the field lies along a river, so only three sides require fencing.
A.) Let x represent the length of the side parallel to the river. Draw a picture of this situation. Be sure to label each side of your rectangle carefully.
B.) Express the area A of the rectangle as a function of x.
C.) Graph A(x) using a graphing utility. For what value of x is the area the largest? Round to the nearest tenth , if applicable. Provide a sketch of what you seen in your grapher, including the window dimensions.
Please help, I'm so lost on this. I can do the graphing part but I'm unsure of how to arrive at the correct answers.
1 Answer
- ?Lv 67 years agoFavorite Answer
Total material available is 2700 ft.
You have Length plus 2 times Width = 2700. So rearrange: Width = (2700 - x)/2, since x has been labeled for the Length.
Area = Length times Width = x(2700 - x)/2 = 1350x - (1/2)x².
So graph this parabola {which opens down}. The peak value occurs at x = 1350