Question

find the length of the altitude of an equilateral triangle of side 4 cm​

Answer 1

Answer:

Let ABC be equilateral triangle

AB=BC =CA =4

Draw perpendicular from A on side BC

Let D be foot of perpendicular

As perpendicular drawn from any vertex of equilateral triangle bisect side opposite to it

So, BD =DC =4/2 = 2

In ∆ADC

AC^2 =AD^2 + DC^2

AD^2 = AC^2 - DC^2

AD^2 = 4^2 -2^2

AD^2 = 16 -4

AD^2 = 12

AD= 2√3

So length of altitude is 2√3cm

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Answer 2

Answer:

Length of altitude of the triangle is 2√3 cm.

Step-by-step explanation:

A median( from any point of the triangle ) divides the triangle into two equal triangles( thus, they are congruent to each other ).

Here,

Side of triangle is 4 cm in length.

Using Pythagoras theorem :

= > ( altitude )^2 + ( half of length of side )^2 = ( side )^2

= > ( altitude )^2 + ( 4 cm / 2 )^2 = ( 4 cm )^2

= > ( altitude )^2 + ( 2 cm )^2 = ( 4 cm )^2

= > ( altitude )^2 = 16 cm^2 - 4 cm^2

= > altitude^2 = 12 cm^2

= > altitude = √12 cm = √( 4 x 3 ) cm = 2√3 cm

Hence, length of altitude of the triangle is 2√3 cm.