Question

Find the altitude of an equilateral triangle of side 10 cm

Answer 1

In Triangle ABC,

AB = BC = AC = 10 cm

BD = BC/2 = 10 / 2 = 5 cm

Now,

In Triangle ABD,

By Pythagoras theoram,

AD^2 = AB^2 - BD^2

AD^2 = 10^2 - 5^2

AD^2 = 100 - 25

AD^2 = 75

AD = 5 root 3

Answer 2

by drawing the perpendicular bisector, we also get the perpendicular height, because the triangle is equilateral. then by the Pythagorean theorem,

                     10^2 = 5^2+h^2
                      h^2  = 10^2-5^2
                              = 100-25
                              = 75


                      h      = sq root of 75 = 5* sq root of 3