Answer:
83
Step-by-step explanation:
When the altitude of a triangle is the perpendicular bisector of the base, that triangle is isosceles. That means QM = SM, which is a relation that lets us find the value of x.
QM = SM
3x +10 = 5x -2
12 = 2x . . . . add 2-3x to both sides
6 = x
The sum of the side lengths is ...
P = QM +SM +QS
P = (3x+10) +(5x -2) +(4x +3) = 12x +11
For x=6, this is ...
P = 12(6) +11 = 72 +11 = 83
The perimeter of the triangle is 83 units.
