Question

HELP ME PLZ 40 POINTS

In Triangle ABC, L is the midpoint of AB, M is the midpoint of BC, and N is the midpoint of CA.
Also, AL = 6, MB = 7, and AC = 24.
What is the perimeter of the Triangle LMN?

Answer 1

∵ M is midpoint of BC, N is midpoint of CA

∴ MN ║ AB

∴ MN = 1/2 AB

∴ MN = 1/2 12 (AB = 6+6, because AL = LB as L is midpoint)

MN = 6cm ---> ( 1 )

∵ M is midpoint of BC, L is midpoint BA

∴ CA ║ LM

∴ LM = 1/2 AC

LM = 1/2 24 = 12cm ---> ( 2 )

∵ L is midpoint AB, N is midpoint of CA

∴ LN ║ BC

∴ LN = 1/2 BC

∴ LN = 1/2 14 (BC = BM + MC because they are equal as M is midpoint)

∴ LN = 7cm ---> ( 3 )

From ( 1 ), ( 2 ) & ( 3 ), The Perimeter of Δ LMN = 7+12+6 = 25cm