Question

Prove that area of an equilateral triangle described on one side of the square is equal to half the area of the equilateral triangle described on one of its diagonal

Answer 1

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Answer 2

Answer:

in triangle ABC , by Pythagoras theorem

AC^2 =AB^2+BC^2:

AC^2=AB^2+AB^2 (ABCD is a Square )

AC^2=2AB^2

Triangle ABC and triangle ACF are equilateral triangle ,

Therefore, these two triangles are equilateral

alright ,triangle ABC is congruent to triangle ACF

ar(ABC) /ar(ACF)= AB^2/AC^2

=AB^2/2 AB^2=1/2 ( AC^2=2AB^2)

Therefore,

ar(ABE)/ ar (ACF)= 1/2

HENCE PROVED