If the area of an equilateral triangle is 36√3 cm², then the length of the side is: Option 1: 12 cm Option 2: 9 cm Option 3: 6 cm Option 4: 3 cm

Answer: 12 cm. Solution: The area of an equilateral triangle with side length a is given by: Area = √3/4 x a^2 Given that the area is 36√3 cm²: 36√3 = √3/4 x a^2 Multiplying both sides by 4: 144√3 = √3 x a^2 Dividing both sides by √3: 144√3/√3 = a^2 144 = a^2 Taking the square root of both sides: a = √144 a = 12 Therefore, the length of the side is 12 cm.

Geometry

Triangles

Medium

If the area of an equilateral triangle is $36\sqrt{3}$ cm², then the length of the side is:

12 cm

9 cm

6 cm

3 cm

✅ Correct Option: 1

The area of an equilateral triangle with side length $a$ is given by:

Area $= \dfrac{\sqrt{3}}{4} \times a^2$

Given that the area is $36\sqrt{3}$ cm²:

$36\sqrt{3} = \dfrac{\sqrt{3}}{4} \times a^2$

Multiplying both sides by $4$ :

$144\sqrt{3} = \sqrt{3} \times a^2$

Dividing both sides by $\sqrt{3}$ :

$\dfrac{144\sqrt{3}}{\sqrt{3}} = a^2$

$144 = a^2$

Taking the square root of both sides:

$a = \sqrt{144}$

$a = 12$

Therefore, the length of the side is $12$ cm.

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Solution

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If the area of an equilateral triangle is $36\sqrt{3}$ cm², then the length of the side is: