Question 456884
First, a right triangle is the breaking point for acute vs obtuse triangle. We find for what x we have a right triangle. There are two scenarios:

Case 1) x and (x+4) are the two feet and 20 is the hypotenuse or
Case 2) x and 20 are the two feet and (x+4) is the hypotenuse

Note that 20 and (x+4) cannot be the 2 feet since x < x+4.

Case 1) {{{x^2 + (x+4)^2 = 20^2}}} --> The solution is x = 12 after discarding -16 as a solution.
Case 2) {{{x^2 + 20^2 = (x+4)^2}}} --> x = 48.

Hence, 12 < x < 48 since, when x = 12, we have a right triangle with sides 12, 16, 20; and when x = 48, we have another right triangle with side 20, 48, 52.