Question

What is the length of the altitude of an equilateral triangle with side a?

Answer 1

Explanation:

As equilateral triangle have equal sides

By applying Pathagores theorem

`(hyp)^2=(per)^2+(base)^2`

by putting values

`(a)^2=(per)^2+( (a)/(2) )^2`

`a^2- (a^2)/(4) =(per)^2`

by taking lcm on L:H:S

`(4a^2-a^2)/(4) =(per)^2`

`(3a^2)/(4) = (per)^2`

by taking square root on both side

`( √(3)a )/(2) =(per)`

i hope u will understand