Question

If the area of equilateral triangle is 3root 3 cmsquare then find the height of equilateral triangle.

Answer 1

Answer:

$Height \: of \:the \: equilateral\\triangle = 3\sqrt{3} \:cm$

Step-by-step explanation:

$Let \: side \: of \: an \\ equilateral \: triangle = a \:cm$

$Area\: of \: triangle (A)\\=3\sqrt{3}\:cm^{2}\:(given)$

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

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

$\implies a^{2}=12$

$\implies a = \sqrt{12}=2\sqrt{3}\: cm$

$Now, \\Height (h) = \frac{3}{2} a\\=\frac{3}{2}\times 2\sqrt{3}\\=3\sqrt{3} \:cm$

Therefore,

$Height \: of \:the \: equilateral\\triangle = 3\sqrt{3} \:cm$

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