ABC is an equilateral triangle of side 4a. Length of its altitude is .
A
2√3a
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B
7√9a
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C
4√3a
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Solution
The correct option is A2√3a
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∘ ∴△ABD≅△ACD (By RHS congruency)
⇒ BD = DC = 2a (by cpct)
In △ABD, AB2=AD2+BD2 (By pythagoras theorm) ⇒AD2=AB2−BD2 ⇒AD2=(4a)2−(2a)2 ⇒AD2=16a2−4a2 ⇒AD2=12a2 ⇒AD=2√3a ∴ Altitude of an equilateral triangle with side 4a will be 2√3a.