Question

AD is an altitude of an equilateral triangle ABC. on AD as base another equilateral angle ADE is constructed.proof that Area(ADE) : Area( ABC) = 3:4.

Answer 1

Given ABC and ADE are equilateral triangles. Let AB=BC=CA = a Recall that the altitude of an equilateral triangle is √3/2 times its side Hence AD = √3a/2 ΔABC �~ ΔADE [By AAA similarity criterion] [Since ratio of areas of two similar triangles is equal to the ratio of their� corresponding sides]  Hence area(ADE):area(ABC)=3:4.

Answer 2

Given ABC and ADE are equilateral triangles.Let AB=BC=CA = a Recall that the altitude of an equilateral triangle is √3/2 times its sideHence AD = √3a/2 ΔABC �~ ΔADE [By AAA similarity criterion] [Since ratio of areas of two similar triangles is equal to the ratio of their� ������������������������������������������������ corresponding sides]  Hence area(ADE):area(ABC)=3:4.