Finding the Hypotenuse of a Right Triangle using the Pythagorean Theorem

To find the length of the hypotenuse, denoted as c, we can use the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, if a=5 and b=12, we can use the formula c = √(a^2 + b^2) to find the length of the hypotenuse.

Plugging in the values, we get c = √(5^2 + 12^2) = √(25 + 144) = √169 = 13. Therefore, the length of the hypotenuse, c, is 13.

This calculation follows the Grade 8 math curriculum in the USA and is an application of the Pythagorean Theorem in the context of geometry.