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
Let fourth side = x. Quadrilateral inequality: each side < sum of other three.
$x<3+2+6=11$ and $6<3+2+x\Rightarrow x>1$. So $x\in\{2,3,4,5,6,7,8,9,10\}$ = 9 values.
$x<3+2+6=11$ and $6<3+2+x\Rightarrow x>1$. So $x\in\{2,3,4,5,6,7,8,9,10\}$ = 9 values.