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

Did you find an error or inaccuracy? Feel free to write us. Thank you!


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.

We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions: