2 sides of a right triangle are 12cm and 13cm. 13cm is the hypotenuse. Use the Pythagorean theorem to estimate the length of the unknown side of the right triangle. Explain why your estimate makes sense and show your work.

The unknown side is 5cm.

The pythagorean theorem states: a² + b² = c²

Where c is the longest side (hypotenuse).

So we plug in and solve for the third side "b".

a = 12, c = 13, so:

12² + b² = 13²

144 + b² = 169

b² = 169 - 144

b² = 25

b = 5

We can double check the pythagorean theorem to make sure:

12² + 5² = 13²

144 + 25 = 169

So the unknown side is definitely 5.