Need help with math please
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Need help with math please

[From: ] [author: ] [Date: 12-03-11] [Hit: ]
25 ft x 83.625 ft.......
Mr. Rogers wants to fence in a rectangular garden next to a straight section of the Scioto
River. He has 330 feet of fencing to do the entire job. He doesn’t need fencing along the
river, and there is a 4.5 foot wide clearance for a gate at one end.
What are the dimensions of the garden (x and y) with the largest area.

Thanks!

-
A standard algebra problem.

Let x = the width and y = the length of the yard.

2x + y - 4.5 = 330
y = 334.5 - 2x

A = xy = x(334.5 - 2x) = 334.5x - 2x^2

This function has a maximum value at its vertex, when x = -334.5/(2(-2)) = 83.625.
y = 167.25

The dimensions of the largest garden in area are 167.25 ft x 83.625 ft.
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