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Question

In an equilateral triangle with side 'a' what is the length of its altitude?

A
a3
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B
2a3
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C
34a
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D
3a2
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Solution

The correct option is D 3a2
In the figure APBC
AB=BC=CA=a
In APB and APC
APB=APC=90
ABP=ACP60 (ABC is equilateral triangle)
By AA similarity
APBAPC
APAP=PBPC=ABAC
PBPC=1PB=PC
PB+PC=a
2PB=a
PB=a2
In APB,APB=90
AB2=AP2+PB2
a2=AP2+(a2)2
AP2=a2a24
AP2=3a24
AP=3a2






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