applications of derviatives

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Tueseve728

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Sep 3, 2005
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Suppose you want to fence in a triangular garden aganst one side of a river. If you have 10 yards of fencing material and you want to enclose the largest possible area. What dimensions should you use for the fence? Be sure to specify the interval over which you will find the absolute max of a functon.

started with A=1/2 bh

Please help, thanks!
 
think it goes a little something like this:

You have 2 equations with the givin information

A=1/2 xy

and

x+y= 10

Solve for y and

x+y=10
y=10-x

substitute into one equation so we only have one variable

A=\(\displaystyle \frac{1}{2}x(10 - x)\)

=\(\displaystyle 5x - \frac{1}{2}x^2\)

take derivitive

A'=5-x

set equal to 0 and solve for x

x-5=0

x=5

therefore since x+y=10

y=5

which makes sence that those dimentions would have the max area.
 
Maybe soneone else can chime in on this one, I'm not exactly sure what you mean. The question is kinda familiar but its been a while since calc 1. Believe me, there is someone here that can anwser that correctly.
 
You've been given a complete worked solution. How much more, exactly, are you needing?

Eliz.
 
Hello, Tueseve728!

This is not a simple problem . . . it is far from solved!
. . (jsbeckton's approach is slightly off.)

Suppose you want to fence in a triangular garden aganst one side of a river.
If you have 10 yards of fencing material and you want to enclose the largest possible area,
what dimensions should you use for the fence?
Click to expand...
Code: 
         B
         *
        /| \
       / |   \y
     x/  |h    \
     /   |       \
  - * - -+- - - - * -
    A    D        C
    |<---  b  --->|
The length of the fencing is: \(\displaystyle x\,+\,y\:=\:10\)

. . But the area is not \(\displaystyle A\;=\;\frac{1}{2}xy\)

The area is: \(\displaystyle \;A\;=\;\frac{1}{2}bh\;=\;\frac{1}{2}(AC)(BD)\)


Besides, knowing that the triangle is isosceles does not help. .Take a look!
Code: 
        *

       * *

     5*   *5
                                *
     *     *              5 *       * 5
                        *               * 
    *-------*       *-----------------------*
 
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