Question

.
If the area of an equilateral triangle is 21.2
sq. cm, find the length of its each side.
​

Answer 1

Answer :-

• Side of Equilateral triangle = 7 cm

Given :-

• Area of Equilateral triangle = 21.2 cm²

To Find :-

• Side of Equilateral triangle = ?

Explanation :-

Let the side of equilateral triangle to be 'x' cm

$\underline { \boxed { \rm \implies \bold { Area \; of \; Equilateral \; triangle = \frac{\sqrt{3} }{4} \; a^2 }}}$

Where,

• a = Side of Equilateral triangle

Now, substituting the values

$\rm \implies Area \; of \; Equilateral \; triangle = \frac{\sqrt{3} }{4} \; a^2 \\ \\ \\ \rm \implies \frac{\sqrt{3} }{4} \; x^2 = 21.2 \; cm^2 \\ \\ \\ \rm \implies \frac{1.73}{4} \; x^2 = 21.2 \; cm^2 \\ \\ \\ \rm \implies x^2 = \frac {21.2 \times 4}{1.73} \; cm^2 \\ \\ \\ \rm \implies x = \sqrt {49} \; cm^2 \\ \\ \\ \underline { \boxed { \rm \bold { \implies x = 7 \; cm }}}$

Hence, the Side of the Equilateral triangle 7 cm.

$\underline { \boxed { \tt \bold {NOTE :} \frac{21.2 \times 4}{1.73} \approx 49 }}$

@Agamsain