Equilateral triangle ABC

In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle contains the triangle KLM.

Correct answer:

x =  0.2778

Step-by-step explanation:

a=1 h=a2(a/2)2=12(1/2)20.866  S=2a h=21 0.8660.433  S1=23h 2a=230.866 210.0722 S2=232 h 2a=232 0.866 210.1443 S3=23h 32 a=230.866 32 10.0962  S4=S(S1+S2+S3)=0.433(0.0722+0.1443+0.0962)0.1203  x=SS4=0.4330.1203=185=0.2778

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