Optimization: Rectangle Inscribed in Triangle

[phyzmatix]

[SOLVED] Optimization: Rectangle Inscribed in Triangle

Homework Statement

Please see http://www.jstor.org/pss/2686484 link. The problem I have is pretty much exactly the same as that dealt with in this excerpt.

(focus on the bit with the heading "What is the biggest rectangle you can put inside a triangle")

Homework Equations

Shown in the link above.

The Attempt at a Solution

I basically want someone to please explain why we need not use a derivative. As you can see, the last sentence is chopped off and leaves me hanging.

 

[konthelion]

We see that x(a-x) is maximum if and only if after completing the square $$(x-\frac{a}{2})^2 =0$$ for when x=? Therefore, the maximum rectangle has a height of what?

 

[konthelion]

Sorry, I didn't really answer your question. You don't need to use the derivative to find the maximum values of x and y because by completing the squares you can find the maximum value of x. Then, you can use x to find the area of that maximum triangle in terms of the area of the triangle.

 

[phyzmatix]

Could you still use a derivative though?

 

[konthelion]

"We need not use a derivative" does not imply that we can't use a derivative to solve for maximum x. So, yes you can use a derivative.

 

[phyzmatix]

"We need not use a derivative" does not imply that we can't use a derivative to solve for maximum x. So, yes you can use a derivative.

Thank you very much for your help konthelion. I'm going to give it a shot using derivatives (I know nothing about completing the squares) and if you don't mind, I'd like you to have a peek at it as soon as I get round to posting it here...

 

[HallsofIvy]

It's very strange that a person would be able to use the derivative (a calculus topic) but not know how to complete the square (an algebra topic).

 

[phyzmatix]

It's very strange that a person would be able to use the derivative (a calculus topic) but not know how to complete the square (an algebra topic).

I know the quadratic equation, but never learned how it was derived (after some googling yesterday, I realized it's the result of completing the square)

Were never taught it in school. Also, there's an eight year gap between the last time I did any maths and starting my BSc in Physics this year...

It's tough going