a^2 + b^2 = c^2
5^2 + b^2 = 13^2
25 + b^2 = 169
b^2 = 144
b = 12
5^2 + b^2 = 13^2
25 + b^2 = 169
b^2 = 144
b = 12
Okay, here's the punchline: using the Pythagorean theorem, we can solve this riddle. The theorem says that the sum of the squares of the two legs is equal to the square of the hypotenuse. So let's do some math magic!
5 squared plus the unknown leg squared equals 13 squared. Simplifying that equation, we get 25 + leg squared equals 169. Now, let's subtract 25 from both sides to isolate the leg: leg squared equals 144. Are you still following along?
Now, my math clown powers tell me that the square root of 144 is 12. So the length of the other leg is 12 cm! Ta-da! We've solved the mystery, and the clown of math strikes again!
Let's call the length of the other leg "a". We know that the length of the hypotenuse is 13 cm, and the length of one leg is 5 cm. Using the Pythagorean theorem, we can set up the following equation:
a^2 + 5^2 = 13^2
Simplifying this equation, we get:
a^2 + 25 = 169
Subtracting 25 from both sides of the equation, we have:
a^2 = 169 - 25
a^2 = 144
Taking the square root of both sides, we get:
a = √144
a = 12
Therefore, the length of the other leg of the right triangle is 12 cm.