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Question

ABC is an equilateral triangle of side 4a. Length of its altitude is .
  1. 23a
  2. 79a
  3. 43a


Solution

The correct option is A 23a


Given: Length of each side of the equilateral triangle = 4a
Construction: Draw a perpendicular from A to BC. Let this meeting point be D.

In ABD and ACD,
AB = AC 
( All sides of an equilateral triangle are equal)
AD = AD (Common)
ADB=ADC=90
ABDACD
(By RHS congruency)

BD = DC = 2a (by cpct)

In ABD,
AB2=AD2+BD2 (By pythagoras theorm)
AD2=AB2BD2
AD2=(4a)2(2a)2
AD2=16a24a2
AD2=12a2
AD=23a
Altitude of an equilateral triangle with side 4a will be 23a.
 

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