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lys-0071 [83]
3 years ago
8

Which of the following sets of possible side lengths forms a triangle?

Mathematics
1 answer:
ki77a [65]3 years ago
7 0
We know that
The triangle inequality states that for any triangle, the sum of the lengths of any two sides of a triangle<span> is greater than the length of the third side
</span>
Part 1) <span>Which of the following sets of possible side lengths forms a triangle?
case A) </span><span>6, 9, and 15
6+9 is not > 15

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

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

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

the answer part 1) is
</span>12, 12, and 23
<span>
Part 2) </span><span>Which of the following sets of possible side lengths forms a right triangle?
</span><span>
case A) </span><span>12, 35, and 38
</span>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,<span>60, and 61
</span>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<span> and 45
</span>if the side lengths forms a right triangle
then
9²+40²=45²
9²+40²------> 1681
45²------> 2025
1681 is not 2025

case D) <span>6, 12, and 13
</span>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) <span>Which of the following sets of sides does not form a right triangle?

case A) </span><span>6, 8, 10
</span>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

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