Question

which of the following sets of numbers could represent the three sides of a triangle? answer {12,19,32} {8,14,24} {5,15,21} {14,24,36} submit answer

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 set {12, 19, 32}

$12 + 19=31<32$, so it cannot form a triangle.

Step3: Check set {8, 14, 24}

$8 + 14 = 22<24$, so it cannot form a triangle.

Step4: Check set {5, 15, 21}

$5+15 = 20<21$, so it cannot form a triangle.

Step5: Check set {14, 24, 36}

$14+24 = 38>36$, $14 + 36=50>24$, $24 + 36 = 60>14$. It can form a triangle.

Answer:

{14, 24, 36}