Question

A gardener has 200 m of fencing to enclose two adjacent rectangular plots. What dimensions will produce a maximum enclosed area?

Answer 1

1. Draw the picture.
2. Formulate the equation.\[A(x)=x(\frac{200-3x}{2})=-\frac{3}{2}x^2+100x\]
3. Note that the function is a parabola opening down, so to find the x value that gives the maximum area, find the x value of the vertex.

Answer 2

the formula of the vertex is a(x-h)2 + k? Am i right? @AnimalAin

Answer 3

The x is 75 :)

Answer 4

Right? @AnimalAin

Answer 5

I get 100/3, with the width 50.

Answer 6

OK, I had a little bit of a computer problem here.... let me try again.

Answer 7

Your formula is related to the vertex, but we need to know the maximum area to make it work. It is probably possible, but cumbersome.

Answer 8

To find the x value of the vertex for y= ax^2 +bx+c, let x=-b/2a. In this case,\[x=\frac{-100}{-3}=\frac{100}{3}\]\[\implies \frac{200-3x}{2}=50\]

Answer 9

Isn't -b=3/2? and a=100

Answer 10

Note that a is the coefficient of the x^2 term, and b is the coefficient of the x term.

Answer 11

Ahhh. :) hmm. Okaay, i forgot. Sorry ^_^v is the x value the last answer? :/

Answer 12

\(-\dfrac{b}{2a} = - \dfrac{100}{2\left( -\frac{3}{2} \right)} =
\dfrac{100}{ 3} \)

Answer 13

I think it asks for the maximum area, which would be A(100/3). You can get it by substitution, or by multiplying the length and width (easier way to get the same answer). I think the answer is about 5000/3 m^2.

Answer 14

Getting late here; gotta get up in the AM. Hope I helped you out. Do math every day.

Answer 15

Thank yoou so much for the help. You really helped alot. Sleep well ^_^v God bless.