Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.
Answers
Answer:
Proof: Any two equilateral triangles are similar because all angles are of 60 degrees. Therefore, area of equilateral triangle described on one side os square is equal to half the area of the equilateral triangle described on one of its diagonals.
Step-by-step explanation:
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Answer:Given :-
→ A square ABCD an equilateral triangle ABC and ACF have been described on side BC and diagonal AC respectively.
To Prove :-
→ ar( ∆BCE ) =
Proof :-
→ Since each of the ∆ABC and ∆ACF is an equilateral triangle, so each angle of his strength is one of them is 60°. So, the angles are equiangular, and hence similar.
==> ∆BCE ~ ∆ACF.
We know that the ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.
[ Because, AC is hypotenuse => AC = √2BC. ]
Hence, it is proved.