A norman window where the semicircle's radius is r (thus the base is 2r) and the height of the rectangle is h. Perimeter is constant, . Show the values r and h are both when the area is a maxiumum.

Please use a method not involving derivatives.

Printable View

- Jun 28th 2010, 03:10 PMjkrowlingProof regarding a norman window max area...
A norman window where the semicircle's radius is r (thus the base is 2r) and the height of the rectangle is h. Perimeter is constant, . Show the values r and h are both when the area is a maxiumum.

Please use a method not involving derivatives. - Jun 28th 2010, 03:46 PMskeeter
- Jun 28th 2010, 04:02 PMjkrowling
OK...

I get to here, but I have trouble further simplifying. - Jun 28th 2010, 04:33 PMskeeter

try again - Jun 28th 2010, 05:39 PMjkrowling
ok...

So then, to prove that this is also the max value for h, I assume I should plug the result into the original equation for h...?

When I simplify this, I get

not the that I was hoping for...?? - Jun 28th 2010, 06:41 PMskeeter

common denominator ...

combine fractions ...

combine like terms ...

simplify ...

you need to work on your algebra.