Question

If the area of an equilateral triangle is 144 under roots 3cm sq , find its perimeter .

Answer 1

$<u><b>Heya mate!! Here's your solution</u>$
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$\huge{Given}$

The area of an equilateral triangle is 144√3 cm².

$\huge{To\: Find}$

The perimeter of the triangle.

$\huge{Solution}$

Area of an equilateral triangle (further mentioned as eq.∆) = 144√3 cm²

But, the area of any eq. ∆ = √3/4 × a² (where a is one of the three equal sides)

Hence, the areas are equal.

=> √3/4 a² = 144√3

=> a² = 144√3 × 4/√3

=> a² = 144 × 4

=> a² = 576

=> a = √576

=> a = 24.

Hence, the side of the eq. ∆ is 24 cm.
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Now, an eq ∆ has all sides equal.

So,

a = b = c = 24 cm (where a,b, c are the sides)
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Now, Perimeter of a triangle

= sum of all sides

= a + b + c

= a + a + a

= 3a

= 3 × 24

= 72 cm

Hence, the perimeter of the eq ∆ is 72 cm.
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$\mathcal{\bold{\pink{Finally,}}}$

Your answer is -

$\boxed{\bold{\mathcal{\red{72\: cm}}}}$
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$\huge{\bold{\mathfrak{\green{Thank\: you}}}}$