October 23, 2000
Problem of the Month

The Triangle Problem
From Twenty Years Before the Blackboard by Michael Stueben

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 the Problem:

Answer is 27.

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

Send any comments or questions to: David Pleacher