Question

AD is drawn perpendicular to base BC of an equilateral triangle ABC.Given BC find the length of AD

Answer 1

Visualizing the question in mind,

In ADB,

AB^2=AD^2+BD^2

since AB=BC, &BD =1/2 BC (by cpct)

BC^2=AD^2+ 1/4 BC^2

AD^2=BC^2 - 1/4BC^2

AD^2 = 3/4 BC^2

Therefore , if BC is given (a side of an equilateral ) ,then,

AD = (√3/2) * (BC)

[For an eqiulateral ABC, whose height, is h or AD]