From statement 2 I understand that 4 can equal any type of height - either one of the three heights which bisects an angle and finishes on the opposite base OR it MIGHT equal the perpendicular height (one of the three side) which we need to find the perimeter. The explanation at the back of the book seems to assume that 4 equals the perpendicular height. Are we allowed to make this assumption? Or is there a way to determine a side from a non-perpendicular height? or is the book wrong?

Thanks

The altitude of a triangle is the perpendicular distance from a vertex to the opposite side.

It may or may not bisect the angle at that vertex (it most likely will not.)

It may or may not be a side of the triangle (it most likely will not).

It may be "inside" the triangle or "outside" the triangle.

- Veritas Help

makes sense thank you