Maths problem: how to do, thanks?

Consider the triangle inequality.

"For a triangle, the sum of the lengths of two sides must be greater than the length of the remaining side."

(Intuitive proof: First point the 3 vertices, named A, B, C. If you want to go from point A to point B, the shortest distance is the length AB. If you first go from A to C, then from C to B, your journey must be longer. Thus AB < AC + CB.)

{ x + 4x > 25
{ x + 25 > 4x
{ 4x + 25 > x

{ 5x > 25
{ 3x < 25
{ 3x > -25

{ x > 5 ...①
{ x < 25/3 ...②
{ x > -25/3 ...③ (this is included in ①)

By ① and ②, 5 < x < 25/3

5 < x ≤ 8

x is an integer, so x can only be 6, or 7, or 8.

The 3 possible different triangles to be form would have length (in cm) (6, 24, 25), (7, 28, 25), and (8, 32, 25).