A rectangular plot of land will be bounded on one side by a river. On the other three sides, it will be bounded by a fence. With 500m of fence to use, what is the largest area you can enclose, and what are its dimensions? (I'm having trouble with this one)

Question

A rectangular plot of land will be bounded on one side by a river. On the other three sides, it will be bounded by a fence. With 500m of fence to use, what is the largest area you can enclose, and what are its dimensions?   (I'm having trouble with this one)

anonymous · Answer

I do know the more closely it becomes a square the larger the area you have.  Let me think on this and get back to you shortly.

anonymous · Answer

A = Length * width
A = lw
500 = 2w + l   solving this for l you get
l = 500 - 2w    substitute that back into the A=lw

A = (500 - 2w)w     distribute
A = 500w - 2w^2   

The maximum can be found at the vertex which you find the w value by -b/2a = -500/-2(2) = w = 125

so I think the width = 125 and the length would be 250

amistre64 · Answer

2x + y = 500

y = 500-2x

area = xy

A = x(500-2x)

anonymous · Answer

I would find the maximum by completing the square, but I'm a badass.

amistre64 · Answer

A = 500x -2x^2

dA = 500 -4x

x = 500/4 = 250/2 = 125

anonymous · Answer

Thank you guys for your help...You are all awesome =D

amistre64 · Answer

y = 500-2x

y = 500 - 2(125)

y = 500 - 250

y = 250

amistre64 · Answer

blext was right...and first :)

anonymous · Answer

LOL

anonymous · Answer

But you did it the "cool" way