Question

AD is altitude of an equilateral triangle ABC on another based AD equilateral triangle ADE is constructed prove that triangle MDE ratio to triangle ABC 3 ratio 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.