Question

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

Answer 1

Step-by-step explanation:

As equilateral triangle have equal sides

By applying Pathagores theorem

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

by putting values

$(a)^2=(per)^2+( \frac{a}{2} )^2$

$a^2- \frac{a^2}{4} =(per)^2$

by taking lcm on L:H:S

$\frac{4a^2-a^2}{4} =(per)^2$

$\frac{3a^2}{4} = (per)^2$

by taking square root on both side

$\frac{ \sqrt{3}a }{2} =(per)$

i hope u will understand