Question

The area of an equilateral triangle is
144√3 cm; find its perimeter.​

Answer 1

Answer:

Given Area of Equilateral triangle = 144 root 3 cm^2.

                   root 3/4 a^2 = 144 root 3

                   a^2 = 144 * 4

                   a^2 = 576

 

                    a = 24.

Perimeter = 3a

                 = 3 * 24

                 = 72.

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Answer 2

Answer:

$\red { Perimeter (P) } \green {= 72 \:cm }$

Step-by-step explanation:

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

$Area \: of \: the \: triangle (A) = 144\sqrt{3} \:cm^{2} \:(given)$

$\implies \frac{\sqrt{3}}{4} a^{2} = 144\sqrt{3}$

$\implies a^{2} = 144\sqrt{3} \times \frac{4}{\sqrt{3}}\\= 144 \times 4$

$\implies a = \sqrt{144\times 4 }\\= 12\times 2 \\= 24 \:cm$

Therefore.,

$\red { Perimeter (P) }$

$\green {= 3a}$

$= 3\times 24 \\= 72\:cm$

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