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If the altitude of an equilateral triangle is 12√3 cm, then its area would be: (SSC CGL 1st Sit. 2015)
- a)12 cm2
- b)72 cm2
- c)36√3 cm2
- d)144√3 cm2
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If the altitude of an equilateral triangle is 12√3 cm, then its ...
Let ΔABC is a equilateral triangle with AD as an altitude from A on side BC.
Let AB = BC = AC = x
From question AD = 12√3 cm.
then from ΔABD,
(AD)2 + (BD)2 = (AB)2
Most Upvoted Answer
If the altitude of an equilateral triangle is 12√3 cm, then its ...
Let ΔABC is a equilateral triangle with AD as an altitude from A on side BC.
Let AB = BC = AC = x
From question AD = 12√3 cm.
then from ΔABD,
(AD)2 + (BD)2 = (AB)2
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Community Answer
If the altitude of an equilateral triangle is 12√3 cm, then its ...
Given:
Altitude of equilateral triangle = 12√3 cm
Formula:
Area of an equilateral triangle = (√3/4) * side^2
Step 1: Find the side length of the equilateral triangle
Given that the altitude of the equilateral triangle is 12√3 cm.
In an equilateral triangle, altitude = (√3/2) * side
Therefore, 12√3 = (√3/2) * side
Solving for side, we get:
side = 24 cm
Step 2: Calculate the area of the equilateral triangle
Using the formula for the area of an equilateral triangle:
Area = (√3/4) * side^2
Area = (√3/4) * 24^2
Area = (√3/4) * 576
Area = 144√3 cm^2
Therefore, the area of the equilateral triangle with an altitude of 12√3 cm is 144√3 cm^2, which corresponds to option 'D'.
Altitude of equilateral triangle = 12√3 cm
Formula:
Area of an equilateral triangle = (√3/4) * side^2
Step 1: Find the side length of the equilateral triangle
Given that the altitude of the equilateral triangle is 12√3 cm.
In an equilateral triangle, altitude = (√3/2) * side
Therefore, 12√3 = (√3/2) * side
Solving for side, we get:
side = 24 cm
Step 2: Calculate the area of the equilateral triangle
Using the formula for the area of an equilateral triangle:
Area = (√3/4) * side^2
Area = (√3/4) * 24^2
Area = (√3/4) * 576
Area = 144√3 cm^2
Therefore, the area of the equilateral triangle with an altitude of 12√3 cm is 144√3 cm^2, which corresponds to option 'D'.
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If the altitude of an equilateral triangle is 12√3 cm, then its area would be: (SSC CGL 1st Sit. 2015)a)12 cm2b)72 cm2c)36√3 cm2d)144√3 cm2Correct answer is option 'D'. Can you explain this answer?
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