Question

Perimeter of equilateral triangle is 24 cm if its height is 6cm. Find its area.

Answer 1

/* There is a mistake in the question. Height is 6cm is wrong */

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

$i) \blue { Perimeter \:of \: the \: triangle }$

$= 24 \:cm \: ( given )$

$\implies 3a = 24 \: cm$

$\implies a= \frac{24}{3}$

$\therefore \green { a = 8 \:cm }$

$ii) \red{Area \: of \: the \: equilateral \: triangle}$

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

$= \frac{\sqrt{3}}{4}\times 8^{2}$

$= \frac{\sqrt{3}}{4}\times 8\times 8$

$= \sqrt{3} \times 8 \times 2$

$= 16\sqrt{3} \: cm^{2}$

Therefore.,

$\red{Area \: of \: the \: equilateral \: triangle}$

$\green { = 16\sqrt{3} \: cm^{2}}$

$iii) If \: Height \: of \: the \: triangle (h) = 6 \:cm$

$\implies \frac{\sqrt{3}}{2} \times a = 6$

$\implies a = \frac{12}{\sqrt{3}} \: --(1)$

$iv )\red{Area \: of \: the \: equilateral \: triangle}$

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

$= \frac{\sqrt{3}}{4}\times \Big(\frac{12}{\sqrt{3}}\Big)^{2}$

$= \frac{\sqrt{3}}{4}\times \frac{144}{3}$

$= \sqrt{3} \times 12$

$= 12\sqrt{3} \: cm^{2}$

Therefore.,

$\red{Area \: of \: the \: equilateral \: triangle}$

$\green { = 12\sqrt{3} \: cm^{2}}$

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