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?

1 Answer
Jan 22, 2017

2020

Explanation:

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

Let D,E and FD,EandF be the midpoint ofAB,BC and ACAB,BCandAC, respectively.

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

=> DEDE is parallel to AC, and DE=1/2AC=8AC,andDE=12AC=8
Similarly, DFDF is parallel to BC, and DF=1/2BC=7BC,andDF=12BC=7
Similarly, EFEF is parallel to AB, and EF=1/2AB=5AB,andEF=12AB=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