Find x in the following right triangle.

12 dm.

The key to solve this problem is using the Pythagoras theorem given by the formula c² = a² + b², where a, b, and c are the sides of the right triangle.

Solving with the values given in the image:

With a = x , b = 5 dm, and c = 13 dm

(13dm)² = (x)² + (5 dm)²

169 dm² = (x)² + 25 dm²

(x)² = 169 dm² - 25 dm²

(x)² = 144 dm²

x = √144 dm²

x = 12 dm