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!
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!
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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.
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.