In the right triangle above, the lengths of the legs are given. Find x.
The pythagorean theorem won't help you much: do not square 27 and 36, add those ugly numbers, and then wonder how to take a square-root of the resultant four-digit number.
Instead, notice that 27 and 36 have a GCM of 9: 27 = 3(9) and 36 = 4(9), so if we scale down by a factor of 9, we have legs of 3 & 4—in other words, the very familiar 3-4-5 right triangle. The hypotenuse of 5, scaled back up by a factor of 9, is 5(9) = 45 = x.