Discussion
The number of vertices (V), edges (E) and faces (F) of a polyhedron are respectively 10, 15 and x. Then, the value of \((3x - 12)\) is :
Answer: B
The value of 3x - 12 is 9.
Euler's formula for polyhedra links vertices, edges and faces:
\[ \begin{aligned} V - E + F &= 2 \\ 10 - 15 + x &= 2 \Rightarrow x = 7 \\ 3x - 12 &= 21 - 12 = 9 \end{aligned} \]
A polyhedron with 10 vertices, 15 edges and 7 faces is a pentagonal prism. 18 would follow from x = 10, which comes from misreading the formula as F = V, and 7 is the value of x itself rather than of 3x - 12.
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