Question

find the length of side of equilateral triangle having area 729√3cm^2​

Answer 1

Here, the area of the equilateral triangle is given as 729√3cm².

• We've to find the length of the side of the triangle.

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As we know that the formula for finding the area of the equilateral triangle is :

$\: \:$

$\underline{\boxed{\sf\pink{Area_{(equilateral \:triangle)} = \frac{ \sqrt{3} }{4}a {}^{2} }}}$

$\: \:$

$\bigstar \: \underline{ \mathfrak{substituting \: the \: values \: : }}$

$\: \:$

$\sf:\implies \: Area_{(equilateral \:triangle)} = \dfrac{ \sqrt{3} }{4} a {}^{2} \\ \\ \\ \sf:\implies \: 729 \sqrt{3} = \frac{ \sqrt{3} }{4} a {}^{2} \\ \\ \\ \sf:\implies \: a {}^{2} = \frac{729 \cancel{\sqrt{3} }\times 4 }{ \cancel{\sqrt{3}} } \\ \\ \\\sf:\implies \: a {}^{2} = 729 \times 4 \\ \\ \\ \sf:\implies \: a {}^{2} = 2916 \\ \\ \\ \sf:\implies \: a = \sqrt{2916} \\ \\ \\ \sf:\implies \: \underline{\boxed{\mathfrak\purple{a = 54cm}}} \: \bigstar$

$\sf\therefore{\underline{Hence, \: the \: side \: of \: the \: equilateral \: triangle \: is \: \bold{54cm}.}}$

Answer 2

Quéstion:

Find the length of side of equilateral triangle having area 729√3 cm².

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SoLutiOn:

» Area of the triangle = 729√3 cm²

» √3/4 × a² = 729√3

» a² = 729 × 4

» a = 27 × 2

» a = 54 cm

Hence, length of theside of the equilateral triangle is 54 cm.