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For a rangoli competition the four participants of the Indira house draw the following rangoli. They drew a regular hexagon of side $8cm$ and then drew 6 equilateral triangles of the same size.
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(A). What is the length of each side of the equilateral triangle?

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Last updated date: 13th Jun 2024
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Answer
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Hint: Here in this question we are given the information that they had a regular hexagon of side $8cm$ and then drew 6 equilateral triangles of the same size. We need to find the length of each side of the equilateral triangle. From the basic concept, we know that the length of all sides of a regular hexagon is equal and the length of all sides of an equilateral triangle is equal.

Complete step-by-step solution
Given in the question that they had drawn a regular hexagon of side $8cm$ and then drew 6 equilateral triangles of the same size as shown in the figure.
As we know from the basic concept that a regular hexagon means a polygon having six sides of equal length.
Here this length is given as $8cm$.
As we know from the basic concept that an equilateral triangle means a triangle having 3 equal sides in length.
Here 6 equilateral triangles are drawn taking the sides of the regular hexagon as the base which are of $8cm$ length according to the question.
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Since the base of the equilateral triangle and the other 2 sides have the same length.
Here in this case the length of the sides of the triangle will be equal to the length of the base that is the length of the sides of the regular hexagon that is given in the question as $8cm$.
Hence, we can conclude that the length of each side of the equilateral triangle will be $8cm$.

Note: Here we have the equilateral triangle drawn using the sides of the regular hexagon as their base. This point should be noted. If we by mistake took the base as half of the side of the regular hexagon we will end up having a different answer.