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
Accepted Solution
A:
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