Question

Solve the following examples.
(1) Find the height of an equilateral triangle having side 2a.
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Answer 1

Given:

• Side of triangle = 2a

To Find:

• Height of an equilateral triangle = ?

Solution:

Let's understand

Here,side of triangle is given 2a and we have to find height of equilateral triangle.

We know that,

$\Large\sf\red{Height\:of\: equilateral\:triangle = {\frac{√3}{2}×{side}^{2}}}$

According to the question,

Now put the values

$\: \: \: \sf \leadsto \: height \: of \: equilateral \: triangle \: = \frac{ \sqrt{3} }{2} \times 2 \\ \\ \: \: \sf \leadsto \: height \: of \: equilateral \: triangle \: = \frac{ \sqrt{3} }{ \cancel2} \times \cancel2 a\\ \\ \: \: \sf \leadsto \: height \: of \: equilateral \: triangle \: = \sqrt{3a}$

Therefore,Height of equilateral triangle = √3a.