If ABC is equilateral triangle such that bd/bc=1/3 and ce/ca=1/3, af/ab=1/3. Find the ratio of area of the shaded region to area of abc

Question

Mathematics

Annabella Lawrence

2 March, 23:51

If ABC is equilateral triangle such that bd/bc=1/3 and ce/ca=1/3, af/ab=1/3. Find the ratio of area of the shaded region to area of abc

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Answers (2)

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Hugh Reilly · Answer 1

This is a well known math problem also called the Feynman's triangle. If the ABC is equilateral triangle, such that the bd/bc=1/3 and ce/ca=1/3, af/ab=1/3. Then the ratio of the area of the shaded region to area of abc is 60.

This is the work to the problem;

B E2 = C E2 + C B2 - 2. CE. CBcos (60) B E2 = 12 + 32 - 2.1.3 12 BE = 7√ (1)

Taniyah · Answer 2

The question ask to calculate or to find the ration of the shaded region to area of ABC if ABC is equilateral triangle. Based on my calculation and further formulation, I came up with an answer of 1/7. I hope you are satisfied with my answer