MIKE finished a job in 3/4hrs.Josh finished the same job in 4/5 of the same time

As we can see, Pythragorean Theorum is being applied in this situation. Pythagorean Theorum is when the sum of two legs of a triangle is equal to the hypotenuse, or the side that's across the right angle (90 degrees).
Pythagorean Theorum is defined in Mathematics by a^2 + b^2 = c^2.

One leg (a) is 5. The other leg (b) is 13.
Let's use Pythagorean Theorum.
5^2 + 13^2 = c^2
5 • 5 = 25
13 • 13 = 169
25 + 169 = 194.

Although the question isn't clearly defining who's correct, the person who chose "Square root 194 equals square root c squared" is correct.

I hope this helps. :)