Question

find the largest of an altitude of an equilateral triangle whose side 6 cm​

Answer 1

Answer:

Let the length of the altitude of an equilateral triangle be xcm

Given the sides of the equilateral triangle is 6cm

From the figure,

x=

6

2

−3

2

=

36−9

=

27

=3

3

∴x=3

3

cm≈5.1961cm

Thus, the altitude of the triangle is 3

3

cm or 5.1961cm

Answer 2

Let the length of the altitude of an equilateral triangle be xcm

Given the sides of the equilateral triangle is 6cm

From the figure,

$x = \sqrt{ {6}^{2} - {3}^{2} }$

$= \sqrt{36 - 9}$

$= \sqrt{27}$

$= 3 \sqrt{3}$

$\bold{\therefore \: x = 3 \sqrt{3} \: cm \approx5.1961 \: cm}$

Thus, the altitude of the triangle is

$3 \sqrt{3} \: cm \: or \: 5.1961 \: cm$