Question

If the area of an equilateral triangle is 36 under root 3 cm square find its height

Answer 1

$\textbf{\huge{\underline{ Hello Mate! }}}$

Since we know that,

Area of equi. triangle = $\frac{\sqrt{3} a^2}{4}$

$36 \sqrt{3} = \frac{ \sqrt{3} {a}^{2} }{4} \\ 36 \sqrt{3} \times \frac{4}{ \sqrt{3} } = {a}^{2} \\ \sqrt{36 \times 4} = a \\ 6 \times 2 = a \\ 12 \: cm = a$

Moreover,

$height = \frac{ \sqrt{3}a }{2} \\h = \sqrt{3} \times \frac{12}{2} \\ h = 6 \sqrt{3} \: cm$

$\textbf{ Have great future ahead! }$