In a triangle ABC, let D and E be the midpoints of AC and BC respectively. The distance from the midpoint of BD to the midpoint of AE is 4.5. What is the length of side AB?
Call F the midpoint of AB. Then the figure has four congruent triangles each half the size of ABC.
Also the midpoint of AE is the midpoint of DF and
the midpoint of BD is the midpoint of EF by smaller congruent triangles.
The given segment is a midsegment of triangle FED.
So DE=2*4.5=9
But DE is a midsegment of triangle ABD
So AD=2*9=18

Posted by Jer
on 20201208 14:22:58 