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AD is an altitude of an …

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AD is an altitude of an equaleteral triangleABC .on AD as base another triangleADE is constructed .prove that area of triangleMDE:area of triangleABCis 3:4

Posted by Sheila Sharma 6 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 6 years, 10 months ago

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/2ΔABC ~ 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.

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CBSE > Class 10 > Mathematics