Which of the following sets of possible side lengths forms a triangle? 6, 9, and 15 4, 10, and 15 10, 15, and 25 12, 12, and 23Which of the following sets of possible side lengths forms a right triangle? 12, 35, and 3811, 60, and 619, 40, and 456, 12, and 13 Which of the following sets of sides does not form a right triangle? 6, 8, 108, 15, 177, 24, 265, 12, 13

we know that
The triangle inequality states that for any triangle, the sum of the lengths of any two sides of a triangle is greater than the length of the third side

Part 1) Which of the following sets of possible side lengths forms a triangle?
case A) 6, 9, and 15
6+9 is not > 15

case B) 4, 10, and 15
4+10 is not > 15

case C) 10, 15, and 25 
10+15 is not > 25

case D) 12, 12, and 23
12+12 is > 23-----> ok
12+23 is > 12----> ok

the answer part 1) is
12, 12, and 23

Part 2) Which of the following sets of possible side lengths forms a right triangle?

case A) 12, 35, and 38
if the side lengths forms a right triangle
then
12²+35²=38²
12²+35²------> 1369
38²------> 1444

1369 is not equal to 1444

case B) 11,60, and 61
if the side lengths forms a right triangle
then
11²+60²=61²
11²+60²-------> 3721
61²------> 3721
3721 is equal to 3721------> the sides forms a right triangle

case C) 9,40 and 45
if the side lengths forms a right triangle
then
9²+40²=45²
9²+40²------> 1681
45²------> 2025
1681 is not 2025

case D) 6, 12, and 13
if the side lengths forms a right triangle
then
6²+12²=13²
6²+12²------> 180
13²--------> 169
180 is not 169

the answer part 2) is 
case B) 11,60, and 61 forms a right triangle

Part 3) Which of the following sets of sides does not form a right triangle?

case A) 6, 8, 10
if the side lengths forms a right triangle
then
6²+8²=10²
6²+8²------> 100
10²-------> 100
100 is equal to 100 ------> the side lengths forms a right triangle

case B) 8,15,17
if the side lengths forms a right triangle
then
8²+15²=17²
8²+15²------> 289
17²-------> 289
289 is equal to 289-----> the side lengths forms a right triangle

case C) 7,24,26
if the side lengths forms a right triangle
then
7²+24²=26²
7²+24²------> 1176
26²--------> 676
1176 is not 676-----> the sides lengths does not form a right triangle

case D) 5,12,13
if the side lengths forms a right triangle
then
5²+12²=13²
5²+12²-------> 169
13²-------> 169
169 is equal to 169------>  the side lengths forms a right triangle

the answer Part 3) is
the option 7,24,26 does not form a right triangle