Finding Maximum Area of Inscribed Rectangle in a Triangle Using Differentiation

[theCandyman]

I recently had a calculus midterm, but was baffled at how to even start this question. Can anyone point me in the direction to start it? It deals with the maximum/minimum section using differentiation.

What is the maximum area of a rectangle inscribed within a triangle with sides 12, 16 and 20?

 

[Tom McCurdy]

this may be of some help
http://jwilson.coe.uga.edu/emt725/Maxrecttri/Maxrecttri.html

 

[theCandyman]

That is so ironic, I go to Georgia Tech. Everyone here is always bashing UGA about being a school of dumb people. I appreciate it, but I was hoping for a more direct help, such as the set up for the equation. I know A = bh, but what do I take the deritive with respect to?

 

[galois427]

begin by drawing a picture. center the triangle on the xy plane. draw an arbitary inscribed rectangle and label the point where the triangle and rectangle meet as (x,y). you should also have a symmetric point labeled (-x,y). find relationship between y and x (using the length of the 3 sides of the triangle). express the area for the rect in terms of x, differentiate, set to zero, and solve.