## Computer Geek seeks Math Nerd

So today I was having a discussion about shipping a TV somewhere and wanted to use the UPS/FedEx cost estimator but didn't want to go measure an actual TV. So I thought to myself I took Algebra I should be able to figure this out quickly. An hour later and I'm frustrated and can't figure out what I've done wrong.

I assume we're all familiar with the Pythagorean Theorem which can be expressed as follows:

This basically means that given any two sides of a right triangle we should be able to find the third. The problem is that I only know the diagonal. I do however know that this is a wide screen TV so I know the ratio of the sides. So I know that the following ratio is true.

Do a little cross multiplication and I get...

Solving for b I get the following.

In theory I should be able to substitute this back into the original Pythagorean formula to get the following.

Now substitute the diagonal width into c and we get the following.

Now turning my attention to the fraction in the middle... Since anything squared is itself times itself I rewrite...

Then I multiple the numerators and the denominators.

Substitute that back in, and square the 46 and I get the following new formula.

Next I multiplied everything by 256 to eliminate the fraction.

Then I added the two left hand operators and reduced to the following.

I divided both sides by 337 (and rounded)...

I then took the square root of both sides (and rounded) to get...

And I'm completely baffled... if this is true then given a diagonal of 46 inches I come up with one side of 2.5 inches which totally does not pass the sanity test. That said I'm completely confused on what I did wrong. Mind you this is using math I haven't touched in probably 10 years so I don't feel too bad.

Any ideas on what I did wrong?