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(C) Let the side of the original equilateral triangle be $x$.The area of the original triangle is given by $A = \frac{\sqrt{3}}{4} x^2$.The side of th

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$36$

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(C) Let the side of the original equilateral triangle be $x$.The area of the original triangle is given by $A = \frac{\sqrt{3}}{4} x^2$.The side of the smaller equilateral triangle is $\frac{x}{6}$.The area of one smaller equilateral triangle is $A_{small} = \frac{\sqrt{3}}{4} 	imes (\frac{x}{6})^2 = \frac{\sqrt{3}}{4} 	imes \frac{x^2}{36}$.The number of smaller triangles formed is the ratio of the original area to the area of one smaller triangle:Number of triangles $= \frac{A}{A_{small}} = \frac{\frac{\sqrt{3}}{4} x^2}{\frac{\sqrt{3}}{4} 	imes \frac{x^2}{36}} = 36$.

An equilateral triangle is cut up into smaller equilateral triangles with side $1/6$ of the original. Find the number of triangles thus formed?

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