I wasnt sure how to solve this question
First of all, it is essential to figure out what x is. After that, we will know the angles in the triangle and will be able to relate m^2 + p^2 to n^2.
We know that the interior angles of a triangle sum to 180 degrees, so x + 3x + 5x = 180 → 9x = 180 → x = 20.
Thus, we know that 5x = 5(20) = 100 and 3x = 3(20) = 60.
We will arrive at the solution by considering the three cases that cylverixxx suggested and finding a contradiction to rule two of the three cases out:
(1) If p^2 +m^2 = n^2, then this triangle would be a right triangle, but we know what the angles are and none of them are 90 degrees. This is a contradiction. Thus, we can rule this case out.
(2) If p^2 + m^2 > n^2, then this triangle would be acute. However, we note that the triangle contains a 100 degree angle, making it an obtuse triangle, so this is a contradiction.
Thus, we know that p^2 + m^2 < n^2.
I hope that helps