Ihave a test on the pythagorean theorem and dilations on dilations could you plz me understand it and how to find the algebraic expressions for them plz?

The Pythagorean Theorem is: 

So, for your problem, the hypotenuse is 13 and another side length is 5.
It doesn't matter if you put 5 in the equation as a or b. 

The equation would be: 
To solve you would do 5*5=25 and 13*13= 169.
You would end up with: 
Subtract 25 from 169 to get 144. In order to get b by itself, you must square root both sides. The other side length is 12.

Then multiply 12 by 5 to get 60
Then divide 60 by 2 to get 30. 
THE ANSWER IS 30.