Answer to October 23, 2000 Problem

From Twenty Years Before the Blackboard by Michael Stueben

The Triangle Problem

 
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