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