Question

the area of an equilateral triangle is 144 square root 3 cm square find its perimeter
$144 \sqrt{3cm {}^{2} }$

Answer 1

Area of an equilateral triangle of side a is given as √3/4 a^2

$\Rightarrow \frac{ \sqrt{3} }{4} {a}^{2} = 144 \sqrt{3} \\ \\ \Rightarrow {a}^{2} = 144 \sqrt{3} \times \frac{4}{ \sqrt{3} } \\ \\ \Rightarrow a = \sqrt{144 \times 4} \\ \\ \Rightarrow a = 24 \: cm$

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

Answer 2

_______Heyy Buddy ❤_______

_______Here's your Answer...______

Given,

Area of Equilateral Triangle =
$144 \sqrt[]{3}$
Now,

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


$1 \div 4 {a}^{2} = 144 \sqrt{3} \div \sqrt{3}$


${a}^{2} = 144 \times 4$

${a}^{2} = 576$

$a = 24$

Now,

Side of an equilateral Triangle = 24cm.

Therefore,

Perimeter of Equilateral Triangle = 3×a

=> 3 × 24

=> 72 cm.
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