Given triangle ABC , AB=3x+4 , BC=2x+5 , and AC=4x determine the x values

Question

Determine the x values

Answer 1

The perimeter=sum of sides=9x+9=9(x+1). There is no other property of the triangle to equate an expression of x. The perimeter or area value would be sufficient. For example, if the perimeter was 72, x=7 (25,19,28).

If the triangle is isosceles then AB=AC, AB=BC or AC=BC. This would enable us to calculate x (AB,BC,AC) respectively: 4 (16,13,16),1 (7,7,4), 2.5 (11.5,10,10).

If the triangle is right-angled, there are no rational solutions for x.