Posted by **Sandy** on Saturday, March 10, 2012 at 6:32pm.

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 doesnâ€™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!

- Math -
**Reiny**, Saturday, March 10, 2012 at 11:04pm
let the width be x

and the length be y

so we are given ....

2x - 4.5 + y = 330

y = 334.5 - 2x

area = xy

= x(334.5-2x)

= 334.5x - 2x^2

d(area)/dx = 334.5 - 4x = 0 for a max area

4x = 334.5

** x = 334.5/4 = 83.625
**

y = 334.5 - 2(83.625) = 167.25

check:

167.25+83.625+83.625-4.5 = 330

area = xy = 13986.28125

let x = 83 , then y = 168.5

area = 13985.5 , a bit smaller

let x = 84 , then y = 166.5

area = xy = 13986 , also a bit smaller than the above

answer looks good.

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