Geometry Triangles

Please have a look at this question. This was a homework from Geometry session 1. Here i had applied “Angle size relationship of a triangle”

Since 5x degree will have the greatest degree then that would make n to be the highest side. With the same logic it becomes n>m>p

Now if i choose numbers then suppose n = 4, m = 3, p = 2 then n^2 is greater.

But if i choose numbers like n = 4, m = 3.9 and p = 3.7, then n^2 is smaller than (m^2+p^2).

Thats how i had arrived to option D as the answer. Can anyone help me where am i going wrong?

Yes, but that doesn’t help you here

A triangle with those side lengths does not have angles of 100, 60, and 20.