how do i figure out the right of a triangle when ab equals 13 and cb equals 12

Guest Jul 12, 2014

#1**+11 **

Best Answer

I do not know what you mean by right of the triangle but I am going to asume you mean the altatude of the right triangle. We will be using the Pythagorean theorem (altitude^2+adjacent^2=hypotenuse^2)

Rose98
Jul 12, 2014

#4**+3 **

Very nice Rose98 !!!..... Good explanation and pic.......thumbs-up and points from me !!!

CPhill
Jul 12, 2014

#5**0 **

5,12,13 is an example of a pythagorean triad

Some other examples include

10,24,26,

20, 48,56,

In fact any three numbers in the same ratio as 5,12, and 13 will be a pythagorean triad

I'll bundle them together and call them 5n, 12n, 13n

Others include

3,4,5 and 3n,4n,5n.

and theere are many more.

This has got me thinking,

Can pythagorean triads only include rational numbers? what kinds of numbers can they include?

Maybe any at all so long as they obey the realtionship $$a^2+b^2=c^2$$ ?

Can they even be imaginary numbers?

I have not googed this - maybe someone would like to google it for me? Then they could share the answer with all of us.

Melody
Jul 13, 2014

#6**+5 **

Melody, I believe - but I'm not sure - that we can generate some Pythagorean Triple "Fractions", using the Pythagorean Triples themselves!!!......I just played around with this a second ago, so I don't really know if it's true - but it seems like it might be.

Let a and b be the first two numbers of any Pythagorean Triple.

Now square them, and write them as denominators of two fractions, each having a numerator of 1. So we have:

1/a^{2} + 1/b^{2} =

(b^{2} + a^{2} ) / (a^{2}* b^{2}) =

(b^{2} + a^{2} ) / (a * b)^{2}

Note that the numerator is a perfect square (the square of the last number in the triple, c) and the denominator is a perfect square, too!!

Therefore:

(1/a)^{2} + (1/b)^{2} = (c/ab)^{2}

And there's a "Pythagorean Triple" Fraction.....!!!!

CPhill
Jul 13, 2014