In an equilateral triangle with side $a$ , prove that altitude is $\frac{\sqrt{3} a}{2}$ .

Open in App

Solution

In $△ A B D, a^{2} = h^{2} + (\frac{a}{2})^{2}$
$h^{2} = a^{2} - \frac{a^{2}}{4} = \frac{3 a^{2}}{4}$
$h = \frac{\sqrt{3} a}{2}$

Suggest Corrections

Similar questions

If ABC is an equilateral triangle of side a, prove that its altitude $= \frac{\sqrt{3}}{2} a$ [3 MARKS]

If ABC is an equilateral triangle of side a, prove that its altitude = $\frac{\sqrt{3}}{2}$ a

A B C

A D

A

B C

3 {A B}^{2} = 4 {A D}^{2}

a

A l t i t u d e = \frac{a \sqrt{3}}{2}

A r e a = \frac{\sqrt{3}}{4} a^{2}

Join BYJU'S Learning Program