Answer is EG = 9 m.
Step by step
We know the two triangles are similar
We are looking for EG (x)
Line AB is similar to EF with ratio 100/90
Line AC is similar to EG with ratio 10/x
So if they are similar we can do our equation as 100/90 = 10/x
Cross multiply
100x = 900
Divide both sides by 100 to solve for x
100/100 x = 900/100
x = 9
My triangles in my attachment are not drawn to size but this is how I find which sides are similar for my equation
I hope this helps