Given scalene triangle PMN.
Segment MX bisects Angle PMN.
Segment NX bisects angle PNM.
Segment QR passes through point X and is parallel to segment MN.
If PM = 10, and MN = 15, and PN = 17, then what is the perimeter of triangle PQR?

Solution to Problem:

Answer is 27.

Solution:
Since triangles QMX and RNX are both isosceles, we have QX = QM and XR = RN.
So the perimeter = PQ + QX + XR +RP
= (PQ + QM) + (PR + RN)
= PM +PN = 10 + 17.



Correctly solved by:

1. Kirstine Wynn Winchester, VA
2. Erin McGinnis Winchester, VA