Question

if the length of each side of an equilateral triangle is 4 cm then what is the length of its median?​

Answer 1

Answer:

the length of the median is 2√3 cm .

Step-by-step explanation:

if we draw a median of equilateral triangle then the triangle will get divided into two equal right angled triangle and the side to which the median is perpendicular is also divides into two equal sides of length 2 cm .

now see in one of he two equal right angled triangles we got

hypotenuse = 4cm

base = 2cm

perpendicular = x cm

now by Pythagoras method

( H )^2 = ( B )^2 + ( P ) ^2

now put values

( 4 )^2 = ( 2)^2 + ( x )^2

16 cm^2 = 4 cm^2 + ( x )^2

16cm^2 - 4cm ^2 = (x)^2

12 cm^2 = ( x)^2

√ 12cm^2 = x

√ 3 * 4 * cm^2 = x

√3 * √4 *√cm^2 = x

2 * √3 * cm = x ( √4 = 2cm )

2√3cm = x

so we got the length of the median .

Answer 2

Answer:

2√3 cm

Step-by-step explanation:

Median of equalatiral triangle = height of the equalatiral triangle = √3/2 a units

= √3/2 × 4 units

= 2√3 cm