A geometry problem by Abhinav Jha

Geometry Level pending

The number of rectangles that can be obtained by joining four of the 12 vertices of a 12-sided regular polygon is __________ \text{\_\_\_\_\_\_\_\_\_\_} .


The answer is 15.

Abhinav Jha by Abhinav Jha , 24, India

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3 solutions

Jesse Nieminen
Sep 13, 2016

We can choose 2 2 non-opposite vertices in 12 ⋅ 10 2 = 60 \dfrac{12\cdot10}2=60 ways.

Each such pair of vertices represents an unique side of a rectangle.

Since rectangle has 4 4 sides, we have 60 4 = 15 \dfrac{60}4=\boxed{15} rectangles.

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Prince Loomba
Sep 13, 2016

6 pairs of opposite sides that are parallel are present. Choose any 2 of them to get rectangle. Answer is 6C2 or 15

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Abhinav Jha
Sep 13, 2016

there are 6 diagonals possible. And out of these 6 we can have 6C2 no of rectangles.

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90% easy according to the topic I am telling

Prince Loomba - 4 years, 9 months ago

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