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Three of the six vertices of a regular h...

Three of the six vertices of a regular hexagon are chosen the random. What is the probability that the triangle with these vertices is equilateral.

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To solve the problem of finding the probability that a triangle formed by randomly selecting three vertices from a regular hexagon is equilateral, we can follow these steps: ### Step 1: Understand the Structure of the Hexagon A regular hexagon has 6 vertices. We can label them as A, B, C, D, E, and F. ### Step 2: Calculate the Total Ways to Choose 3 Vertices We need to find the total number of ways to choose 3 vertices from 6. This can be calculated using the combination formula: ...
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Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral equals :

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Knowledge Check

  • Three vertices are chosen at random from the vertices of a regular hexagon then The probability that the triangle with these vertices is an equilateral triangle is equal to

    A
    `1/10`
    B
    `3/5`
    C
    `9/10`
    D
    `3/10`

  • If three vertices of a regular hexagon are chosen at random, then the chance that they form an equilateral triangle is :

    A
    `1/3`
    B
    `1/5`
    C
    `1/(10)`
    D
    `1/2`

  • If three vertices of a regular hexagon are chosen at random, then the chance that they form an equilateral triangle is :

    A
    `1/3`
    B
    `1/5`
    C
    `1/10`
    D
    `1/2`

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