Question

which of the following sets of numbers could not represent the three sides of a triangle? answer {5,11,13} {15,25,42} {10,20,29} {12,22,32}

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 {5, 11, 13}

$5 + 11=16>13$, $5 + 13 = 18>11$, $11+13 = 24>5$. So it can form a triangle.

Step3: Check {15, 25, 42}

$15 + 25=40<42$. So it cannot form a triangle.

Step4: Check {10, 20, 29}

$10 + 20 = 30>29$, $10+29 = 39>20$, $20 + 29=49>10$. So it can form a triangle.

Step5: Check {12, 22, 32}

$12+22 = 34>32$, $12 + 32=44>22$, $22+32 = 54>12$. So it can form a triangle.

Answer:

{15, 25, 42}