Ratio of triangles areas

In an equilateral triangle ABC, the point T is its centre of gravity, the point R is the image of the point T in axial symmetry, along the line AB, and the point N is the image of the point T in axial symmetry along the line BC. Find the ratio of the areas of the triangles ABC and TRN.

Correct answer:

r =  3:1

Step-by-step explanation:

a=1 v=3/2 a=3/2 10.866  S1=2a v=21 0.8660.433 t1:t2=2:1 t1+t2=t=v  t2=31 v=31 0.8660.2887  TR=2 t2=2 0.28870.5774 TN=TR=0.57740.5774  BTN=60   cosBTN=v2:TN v2=TN cosBTN°=TN cos60° =0.5774 cos60° =0.5774 0.5=0.28868  TN2=(RN/2)2+v22 RN=2 TN2v22=2 0.577420.28872=1  S2=2RN v2=21 0.28870.1443  r=S1/S2=0.433/0.1443=3=3:1



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Tips to related online calculators
Check out our ratio calculator.
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

 
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