Question

Please solve this fast ​

Answer 1

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 .