# Wikijunior:More on Mathematics/Pythagorean theorem

The Pythagorean theorem is the theory that the sum of the square areas of sides A and B add up to the hypotenuse, or C's square area. It's formula is described as:

${\displaystyle a^{2}+b^{2}=c^{2}}$

There are many reasons to prove this correct; you may find them on Wikipedia. However, there is more than just this equation, called the Pythagorean equation.

## Pythagorean triples

Pythagorean triples are three sets of positive whole numbers that can make a perfect triangle.

Take the image on the right. Pretend ${\displaystyle a}$  is 3 and ${\displaystyle b}$  is 4. What is ${\displaystyle c}$ ? (Hint: ${\displaystyle c}$  is the hypotenuse; the longest side on the picture.) Use the Pythagorean equation to figure it out! (Click on the reference link to see the answer!)[1]

Now, let's try the Pythagorean equation backwards! Now, ${\displaystyle b}$  is 12 and ${\displaystyle c}$  is 13. Please figure out ${\displaystyle a}$ .[2]

## Unsquare the sides

Take the image on the right again. Let's pretend that (A) is 5, (B) is 8, what would be C?

${\displaystyle a^{2}+b^{2}=c^{2}}$

${\displaystyle 5^{2}+8^{2}=c^{2}}$

${\displaystyle 25+64=c^{2}}$

${\displaystyle 89=c^{2}}$

Now we want to know the real length of the C side. As we can see, c is squared, now we need to unsquare the ${\displaystyle c^{2}}$ , we do this by doing a square root, like ${\displaystyle {\sqrt {x}}}$ . In math, ${\displaystyle x}$  is usually used to represent an unknown variable.

So now,

${\displaystyle {\sqrt {89}}={\sqrt {c^{2}}}}$ , the square and the square root cancel out.

So we're left with,

${\displaystyle 9.43398113206=c}$

Now we know that if side ${\displaystyle a}$  is 5, and ${\displaystyle b}$  is 8, ${\displaystyle c}$  is 9.43398113206.