Question

Q.14 Find the side of an equilateral triangle whose area is 12√3cm²​

Answer 1

Answer:

4

$\frac{1}{2}$

Answer 2

$let \: the \: side \: of \: equilateral \: triangle \: = x \\ (ad) {}^{2} + ( \frac{x}{2} ) {}^{2} = (x) {}^{2} \\ (ad) {}^{2} = (x) {}^{2} - ( \frac{x}{2}) {}^{2} \\ (ad) {}^{2} = x {}^{2} - \frac{x {}^{2} }{4} \\ (ad) {}^{2} = \frac{3x {}^{2} }{4} \\ ad = \sqrt{ \frac{3x {}^{2} }{4} } \\ ad = \sqrt{3} \frac{x}{2} \\ area \: of \: triangle \: = \frac{1}{2} \times base \times height \\ 12 \sqrt{3 } = \frac{1}{2} \times x \times \sqrt{3} \frac{x}{2} \\ x = \sqrt{48} \\ x = 4 \sqrt{3}$

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