To find the length of the hypotenuse in a right triangle, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the two legs (a and b). The formula is:
c² = a² + b²
In this case, the lengths of the legs are 5 and 12. We can plug these values into the formula:
c² = 5² + 12²
This simplifies to:
c² = 25 + 144
So:
c² = 169
Now, to find the hypotenuse, we take the square root of both sides:
c = √169
Calculating this gives:
c = 13
Therefore, the length of the hypotenuse of the right triangle is 13.