#### Question

Find the length of the side and perimeter of an equilateral triangle whose height is \[\sqrt{3}\] cm.

#### Solution

Since, ABC is an equilateral triangle, CD is the perpendicular bisector of AB.

Now, According to Pythagoras theorem,

In ∆ACD

\[{AC}^2 = {AD}^2 + {CD}^2 \]

\[ \Rightarrow \left( 2a \right)^2 = a^2 + \left( \sqrt{3} \right)^2 \]

\[ \Rightarrow 4 a^2 - a^2 = 3\]

\[ \Rightarrow 3 a^2 = 3\]

\[ \Rightarrow a^2 = 1\]

\[ \Rightarrow a = 1 cm\]

Hence, the length of the side of an equilateral triangle is 2 cm.

Now,

Perimeter of the triangle = (2 + 2 + 2) cm

= 6 cm

Hence, perimeter of an equilateral triangle is 6 cm.

Is there an error in this question or solution?

Solution Find the Length of the Side and Perimeter of an Equilateral Triangle Whose Height is √ 3 Cm. Concept: Similarity in Right Angled Triangles.