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:

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

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 $a$ is 3 and $b$ is 4. What is $c$? (Hint: $c$ 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!)

Now, let's try the Pythagorean equation backwards! Now, $b$ is 12 and $c$ is 13. Please figure out $a$.

Unsquare the sides

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

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

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

$25+64=c^{2}$

$89=c^{2}$

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 $c^{2}$, we do this by doing a square root, like ${\sqrt {x}}$. In math, $x$ is usually used to represent an unknown variable.

So now,

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

So we're left with,

$9.43398113206=c$

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