Question

if the area of an equilateral triangle is 36√3 cm square find the length ​

Answer 1

Answer:

Let the sides of equilateral triangle be "s" cm. => s/2 = √36 cm or 6 cm. => s = (6×2) cm = 12 cm.

Answer 2

${\blue{\underline{\underline{\purple{\textsf{\textbf{Answer : }}}}}}}$

➙ The length (each side) of the equilateral △ is 12cm. ${\boxed{\green{\checkmark{}}}}$

${\blue{\underline{\underline{\purple{\textsf{\textbf{Step-by-step explanation: }}}}}}}$

✦ Using the formula :

${\pink{\sf{\longrightarrow{Area \: of \: the \: \triangle = \frac{ \sqrt{3} }{4} {a}^{2}}}}}$

• $a$ represents each side of the triangle.

$\begin{gathered} { \textsf{ \textbf{Here}}} \begin{cases} \sf{Area \: of \: the \: \triangle \: \to \: 36\sqrt{3}cm^2 (given)} \end{cases} \end{gathered}$

So,

$: \sf \implies \: 36\sqrt{3} = \frac{ \sqrt{3} }{4} {a}^{2}$

$: \sf \implies \: \frac{4 \times 36 \sqrt{3} }{ \sqrt{3} } = {a}^{2}$

$: \sf \implies \: 4 \times 36 = {a}^{2}$

$: \sf \implies \: \sqrt{4 \times 36} = a$

$: \sf \implies \: 2 \times 6 = a$

$: \sf \implies \: a = 12cm$

${\therefore{\underline{\underline{{\textsf{\textbf{The length of the equilateral △ is 12cm: }}}}}}}$