Question

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 23

Which 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, 26 5, 12, 13

Answer 1

12,12, and23

Explanation:

Answer 2

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