Mathematics, 21.07.2019 22:30 terryhgivens5349

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

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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

Answer from: Quest

180

step-by-step explanation:

Answer from: Quest

Agc and bgd are vertical angles

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