Co-ordinate geometry minimum problem?

**The area of a rectangular block of land is 1000m**^{2}. If its length is x metres, find the block's dimensions if the perimeter is a minimum?

I have to solve the problem using a composite graph and finding its minimum rathert than using calculus. It would be appreciated if you could help me as I'm really not sure how to approach this :)

- iamapineapple

Re: Co-ordinate geometry minimum problem?

Letting $\displaystyle x$ be the length, I would then let $\displaystyle y$ be the width, $\displaystyle A$ be the area, and $\displaystyle P$ be the perimeter.

Can you give the area and perimeter in terms of $\displaystyle x$ and $\displaystyle y$?

Re: Co-ordinate geometry minimum problem?

Thank you, I am so silly. I got to the stage of making an equation for the perimeter but broke down because I didn't know what to let it equal to (i.e. thanks to you, I just let it equal P and **then **subbed values)!

Thanks, I got the (easy) answer!

Re: Co-ordinate geometry minimum problem?

Alternatively you can go as under:

Area = length x breadth

Let length = x m

Thus 1000 = x * breadth : Thus breadth = 1000/x

Perimeter P = 2 ( length + breadth ) = 2 ( x + 1000/x )

now you can take it forward.