2sides 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 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.

The unknown side is 5cm.