Question

The side of an equilateral triangle is 16 cm . Find the length of its altitude. Solve with steps

Answer 1

by drawing altitude AD to a triangle ABC
so we get an right angled triangle ADC right angle at D
so, AC=16, CD=8 and let AD=x
then b pythagoras thorem we get 16²=x²+8²
                                                      256=x²+64
                                                      x²=256-64
                                                      x=√192
                                                      x=8√3cm
therefore, length of the altitude = 8√3 cms

Answer 2

In equilateral triangle ABC, median AD is also the altitude. AB = 16 cm BD = 8 cm Triangle ABD is right angled, So, $AB^{2} = AD^{2} + BD^{2}$ => $AD^{2} = 16^{2} - 8^{2}$ = 256 - 64 = 192 => AD = √192 = 8√3 cm