Wikijunior:More on Mathematics/Pythagorean theorem

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Pythagorean.svg

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:



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[edit]

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

Take the image on the right. Pretend is 3 and is 4. What is ? (Hint: 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, is 12 and is 13. Please figure out .[2]

Unsquare the sides[edit]

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

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 , we do this by doing a square root, like . In math, is usually used to represent an unknown variable.

So now,

, the square and the square root cancel out.

So we're left with,

Now we know that if side is 5, and is 8, is 9.43398113206.

References and answers[edit]

  1. Please highlight to your right: (C) is 5.
  2. Please highlight to your right: (A) is 5. AGAIN?! Oh man, this is cheap! (Actually, no it's not.)