Question

below are side lengths of triangles. which triangle cannot exist based on the triangle inequality theorem? a 2 in, 5 in, 6 in b 3 in, 6 in, 8 in c 2 in, 4 in, 8 in d 5 in, 12 in, 9 in

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step2: Check option A

$2 + 5=7>6$, $2 + 6 = 8>5$, $5+6 = 11>2$. This triangle can exist.

Step3: Check option B

$3 + 6=9>8$, $3 + 8 = 11>6$, $6 + 8=14>3$. This triangle can exist.

Step4: Check option C

$2+4 = 6<8$. The sum of the two shorter sides is less than the longest side, so this triangle cannot exist.

Step5: Check option D

$5+9 = 14>12$, $5 + 12=17>9$, $9+12 = 21>5$. This triangle can exist.

Answer:

C. 2 in, 4 in, 8 in