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The area of an equilateral triangle is \( \Large \Large \frac{\sqrt{243}}{4} \)sq cm. Find the length of its side.

Correct Answer:

A) 3 cm |

B) \( \Large 3\sqrt{3} \)cm |

C) 9 cm |

D) \( \Large \sqrt{3} \)cm |

Correct Answer:

A) 3 cm |

Description for Correct answer:

According to the question,

\( \Large \frac{\sqrt{3}}{4}a^{2}=\frac{\sqrt{243}}{4} \)

=> \( \Large a^{2}=\frac{\sqrt{81\times 3}}{\sqrt{3}}=\frac{9\sqrt{3}}{\sqrt{3}} \)

a=\( \Large \sqrt{9} \)=3cm

According to the question,

\( \Large \frac{\sqrt{3}}{4}a^{2}=\frac{\sqrt{243}}{4} \)

=> \( \Large a^{2}=\frac{\sqrt{81\times 3}}{\sqrt{3}}=\frac{9\sqrt{3}}{\sqrt{3}} \)

a=\( \Large \sqrt{9} \)=3cm

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