Question

Find the perpendicular height of an
equilateral triangle whose side is 12 cm


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Answer 1

Answer:

Step-by-step explanation:The altitude of an equilateral triangle bisects the side on which it stands and forms right-angled triangles with the remaining sides.

So, CD=DB=6cm

Also in △ADC,∠ADC=90  

∘

 

Applying Pythagoras theorem gives

(AC)  

2

=(CD)  

2

+(AD)  

2

 

(12)  

2

=(6)  

2

+(AD)  

2

 

144=36+(AD)  

2

 

(AD)  

2

=108

AD=  

108

​  

=6  

3

​  

cm

The height of equilateral triangle =6  

3

​  

cm