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An equilateral triangle ABC whose side is 15 cm, its corner are cut to form a hexagon PQRSTU with all sides equal and PQ is on base BC. Then, what is the length of side of hexagon?

An equilateral triangle ABC whose side is 15 cm, its corner are cut to form a hexagon PQRSTU with all sides equal and PQ is on base BC. Then, what is the length of side of hexagon? Correct Answer 5 cm 

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Let the side of hexagon be x cm.

Then, SR = x cm

As the sides of hexagon are equal and ΔABC is an equilateral triangle

∴ ΔATS, ΔBUP and ΔQRC are also an equilateral triangle

Thus, RC = AS = SR = x cm

According to question,

AC = AS + SR + RC

⇒ 3x = 15cm

⇒ x = 15/3

⇒ x = 5 cm

So, the side of the hexagon is 5 cm.

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