Question

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

Answer 1

area of equilateral triangle = root 3 a^2/4
put value of a = side = 16
area = 64root3
area of triangle = 1/2×b×h
64root3=1/2×16×h
h=8 root 3

Answer 2

Answer:

The length of altitude is found out to be $8\sqrt3$ cm

Solution:

An equilateral triangle is a triangle which has the all the three sides of equal length.

We know, Area of an equilateral triangle  

$= \frac { \sqrt { 3 } } { 4 } a ^ { 2 }$

Where, a = length of each side  

For the given equilateral triangle,  

a = 16 cm.

∴ Area of the equilateral triangle  

$= \frac { \sqrt { 3 } } { 4 } ( 16 c m ) ^ { 2 } = 64 \sqrt { 3 } c m ^ { 2 }$

And, we know,  

Area of a triangle can also be given as  

$= \frac { 1 } { 2 } \times \text { length of base } \times \text { length of altitude }$

For the given triangle,

$64 \sqrt { 3 } \mathrm { cm } ^ { 2 } = \frac { 1 } { 2 } \times 16 \mathrm { cm } \times \text { length of altitude }$

length of altitude

$= 64 \sqrt { 3 } \mathrm { cm } ^ { 2 } \times \frac { 2 } { 16 }$

Thus, the length of altitude is found out to be $8\sqrt3$ cm