There are 3 right triangles in this problem and they are all similar.

To get your answers, make a table with columns labeled "Long" "Short" and "Hypotenuse"

Use one line of the table for each of the three triangles,

In each box of the table put the identity of the line segment which belongs there

The rows are elements of the proportion you need to answer the questions.

Oh, and one other thing you need: Remember that segment EG + segment FG is segment EF.

Follow these directions and you should be able to prove the Theorem of Pythagoras.