Three sides of a quadrilateral are 3 cm, 2 cm and 6 cm, and the fourth side is an integer. How many lengths are possible for the fourth side?
Answer and solution
Correct answer: C
Solution
Any side must be less than the sum of the other three. Let the fourth side be $x$.
$x < 3 + 2 + 6 = 11$
$6 < 3 + 2 + x \Rightarrow x > 1$
$x \in \{2, 3, \ldots, 10\}$ → $9$ lengths
$x < 3 + 2 + 6 = 11$
$6 < 3 + 2 + x \Rightarrow x > 1$
$x \in \{2, 3, \ldots, 10\}$ → $9$ lengths