Question

Find the area of an equilateral triangle whose
perimeter is 36 cm. Also, find its height.​

Answer 1

Answer:

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Perimeter = 3x=36 cm

x=12 cm

⋆In triangle ABD by pythagoras theorem

${x}^{2} = ( \frac{x}{2})^{2} + {ad}^{2}$

${ad}^{2} = \frac{3x}{4} ^{2}$

$ad = \sqrt{ \frac{3}{2} x}$

$height = \sqrt{ \frac{3}{2} } \times 12 = 6 \sqrt{3}$

$area = \frac{1}{2} \times base \times height$

$\frac{1}{2} \times x \times \sqrt \frac{3}{2} {x}$

$\sqrt \frac{3}{4} { {x}^{2} } = \sqrt \frac{3}{4} \times ({12})^{2}$

$area = 36 \sqrt{ {3cm}^{2} }$

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