Question

Triangle ABC has AB=10, BC=14, and AC=16. What is the perimeter of triangle DEF created by each vertex being the midpoint of AB, BC and AC?

Answer 1

`20`

Explanation:

Given `AB=10, BC=14 and AC=16`,

Let `D,E and F` be the midpoint of`AB,BC and AC`, respectively.

In a triangle, the segment joining the midpoints of any two sides will be parallel to the third side and half its length.

`=> DE` is parallel to `AC, and DE=1/2AC=8`
Similarly, `DF` is parallel to `BC, and DF=1/2BC=7`
Similarly, `EF` is parallel to `AB, and EF=1/2AB=5`

Hence, perimeter of `DeltaDEF=8+7+5=20`

side note : `DE, EF and FD` divide `DeltaABC` into 4 congruent triangles, namely, `DeltaDBE, DeltaADF,DeltaFEC and DeltaEFD`

These 4 congruent triangles are similar to `DeltaABC`