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Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of equilateral triangle described on one of its diagonals |
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Answer» 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, Hence, it is proved. |
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