Answer to Question #158228 in Geometry for Janine

Question

The sides of a triangle are 9, 10, and 14. Find the perimeter of the triangle formed

by joining the midpoints of the three sides.

Answer 1

It is known that the segment of line joining the middle points of two sides of a triangle is parallel to the third side and its lengths is half the third side's.

Thus, the triangle formed by joining the midpoints of the three sides has sides:

$\frac{9}{2}=4.5,\;\frac{10}{2}=5,\;\frac{14}{2}=7.$

And its perimeter: $P=4.5+5+7=16.5.$