Question

which of the following sets of numbers could not represent the three sides of a triangle? answer attempt 1 out of 2 {10,21,29} {4,17,22} {9,20,28} {11,20,29}

Explanation:

Step1: Recall triangle inequality rule

For sides $a,b,c$, sum of any two sides > third side. We only need to check if sum of the two shorter sides > longest side.

Step2: Check set {10,21,29}

$\text{Sum of shorter sides: } 10+21=31$
$31 > 29$, valid triangle.

Step3: Check set {4,17,22}

$\text{Sum of shorter sides: } 4+17=21$
$21 < 22$, violates inequality.

Step4: Verify remaining sets (optional)

For {9,20,28}: $9+20=29 > 28$, valid.
For {11,20,29}: $11+20=31 > 29$, valid.

Answer:

B. {4, 17, 22}