Answer: EP is 12 and EO is about 10.91.
To find the length of EP, we can use the Pythagorean Theorem with the 2 legs of the right triangle it would form, EC and CP. CP would be 5 because it is the midpoint of the side.
5^2 + (EP)^2 = 13^2
EP = 12
Now, to find EO, we write and solve another Pythagorean Theorem equation using 12 for EP.
5^2 + (EO)^2 = 12^2
EO equals the square root of 119 or about 10.91.
