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Answers
Answer :
Altitude , p = 3 cm
Solution :
- Given : Side , a = 2√3 cm
- To find : Altitude , p = ?
We know that ,
The altitude of an equilateral triangle is given by ; p = √3a/2 units .
Hence ,
=> p = √3×2√3 / 2
=> p = √3 × √3
=> p = 3 cm
Hence ,
Altitude , p = 3 cm
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Deduction of the formula for altitude of an equilateral triangle with side a .
Note :
• The altitude of an equilateral triangle bisects the base .
• Pythagoras theorem : In a right angled triangle , h² = p² + b² .
Where h = hypotenuse ( longest side / side opposite to the right angle ) ,
p = perpendicular ( or altitude ) and
b = base .
Now ,
Refer to the attachment for diagram .
Clearly ,
In right ∆ADC , we have ;
• Hypotenuse , h = a
• Altitude = p
• Base , b = a/2
Now ,
Applying Pythagoras theorem in right ∆ACD , we have ;
=> h² = p² + b²
=> a² = p² + (a/2)²
=> a² = p² + a²/4
=> p² = a² - a²/4
=> p² = (3a² - a²)/4
=> p² = 3a²/4
=> p = √(3a²/4)
=> p = √3a/2
Hence ,
The altitude of an equilateral triangle of side a is given as ;
p = √3a/2 .
