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12 January, 23:30

A convex polyhedron has (a + 3) faces, (2a) vertices, and (4a - 1) edges. What is the value of a? a =

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  1. 13 January, 01:06
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    Number of faces: F=a+3

    Number of vertices: V=2a

    Number of edges: E=4a-1

    V+F-E=2

    Replacing V=2a; F=a+3; and E=4a-1 in the formula above:

    (2a) + (a+3) - (4a-1) = 2

    Eliminating parentheses:

    2a+a+3-4a+1=2

    Adding similar terms:

    (2+1-4) a + (3+1) = 2

    (-1) a+4=2

    Solving for a. Subtracting 4 both sides of the equation:

    (-1) a+4-4=2-4

    (-1) a=-2

    Dividing both sides by (-1)

    (-1) a / (-1) = - 2 / (-1)

    a=2

    Answer: The value of a is: a=2
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