Calculate the height of an equilateral triangle each of whose sides measures 12 cm.

Given:

Each side of an equilateral triangle measures 12 cm.

To do: 

We have to find the height of the equilateral triangle.

Solution:

In the above figure, AD is the altitude of the equilateral triangle ABC.

$AB=BC=CA=12\ cm$

In $\triangle ADB$ and $\triangle ACD$,

$\angle ADB=\angle ADC=90^o$

$AB=AC$

Therefore,

$\triangle ADB \cong\ \triangle ACD$    (By RHS congruence)

This implies,

$BD=DC=\frac{BC}{2}=\frac{12}{2}\ cm=6\ cm$     (CPCT)

In $\triangle ADB$,

$AB^2=AD^2+BD^2$    (By using Pythagoras theorem)

$(12)^2=AD^2+(6)^2$

$AD^2=144-36$

$AD^2=108$

$AD=\sqrt{108}\ cm$

$AD=\sqrt{36\times3}\ cm$

$AD=6\sqrt3\ cm$

The height of the equilateral triangle is $6\sqrt3\ cm$.

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Updated on: 10-Oct-2022

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