Question

The area of an equilateral triangle is 9√3 square units. Find the perimeter of the

triangle:

a. 6 b. 36 c. 18 d. 18√3​

Answer 1

Answer:

18

Step-by-step explanation:

√3b² = 36√3 cm² : divide both sides by √3 to isolate b²

b² = 36 cm² : take the square root of both sides to isolate b

b = 6 cm : simplify the radical

So each side is 6 cm

The perimeter is the sum of all three sides: 6 cm + 6 cm + 6 cm = 18 cm.

Answer 2

$\huge\sf{\underline{\underline{\bold{\sf{Given\::}}}}}$

• $\sf{Area\:of\:an\:Equilateral\:Triangle\:=\:9\:\sqrt{3}}$

${ }$

$\huge\sf{\underline{\underline{\bold{\sf{Find\::}}}}}$

• $\sf{Perimeter\:of\:the\:Triangle}$

${ }$

$\huge\sf{\underline{\underline{\bold{\sf{Solution\::}}}}}$

• $\bf{Let\:the\:side\:of\:an\:equilateral\:=\:a\:cm}$
• $\bf{Area\:of\:an\:Equilateral\:Triangle\:=\:9\:\sqrt{3}}$

${ }$

$\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{\frac{\sqrt{3}}{4}}\:\times\:{a}^{2}\:=\:9{\sqrt{3}}$

$\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{a}^{2}\:=\:9{\sqrt{3}}\:\times\:{\frac{4}{\sqrt{3}}}$

$\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{a}^{2}\:=\:9\:\times\:4$

$\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{a}^{2}\:=\:36$

$\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{a\:=\:{\sqrt{36}}}$

$\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{a\:=\:6\:cm}$

${ }$

• $\small\sf{Now,\:Perimeter\:of\:the\:equilateral\:triangle\:=\:3a}$

$\:\:\:\:\:\:\:\::\:\Longrightarrow\sf{\:3\:\times\:6}$

$\:\:\:\:\:\:\:\::\:\Longrightarrow\sf{\:18\:cm}$

${ }$

$\:\:\:\:\:\:\:\:{\purple{\bold{\dag}}}\:{\underline{\sf{So,\:the\:correct\:option\:c\:is\:{\bold{\pink{18\:cm}}}}}}.$