Question

Which list shows the lengths of three line segments that could not form a triangle

Answer 1

$To \ build \ a \ triangle \ with \ these \ segments, \ \\ \\ must \ be \ the \ condition:$

$a+b >c \\ a+c>b \\ b+c>a$



$a =6 \ cm, \ \ b= 8 \ cm, \ \ c =10 \ cm \\6 \ cm+8 \ cm>10 \ cm \\6 \ cm+10 \ cm>8 \ cm\\8 \ cm+10 \ cm>6 \ cm \\ \\14 \ cm >10 \ cm \\16 \ cm >8 \ cm \\18 \ cm > 6 \ cm \\ \\ are \ line \ segments \ that \ form \ a \ triangle$



$a =5 \ cm, \ \ b= 6 \ cm, \ \ c =7 \ cm \\5 \ cm+6 \ cm>7 \ cm \\5 \ cm+7\ cm>6 \ cm\\6 \ cm+7 \ cm>5 \ cm \\ \\11 \ cm >7 \ cm \\12 \ cm >6 \ cm \\13 \ cm > 5 \ cm \\ \\ are \ line \ segments \ that \ form \ a \ triangle$



$a =4 \ cm, \ \ b= 7 \cm, \ \ c =13 \cm \\4\ cm+7 \ cm>13 \ cm \\4 \ cm+13\ cm>7 \ cm\\7 \ cm+13 \ cm>4 \ cm \\ \\11 \ cm < 13 \ cm \\17 \ cm >6 \ cm \\20\ cm > 4 \ cm \\ \\ are \ line \ segments \ that \ cannot \ form \ a \ triangle$



$a =3 \ cm, \ \ b= 6 \cm, \ \ c =6 \cm \\3\ cm+6 \ cm>6 \ cm \\3\ cm+6\ cm>6\ cm\\6 \ cm+6\ cm>3 \ cm \\ \\9 \ cm > 6\ cm \\9 \ cm >6 \ cm \\12\ cm > 3 \ cm \\ \\ are \ line \ segments \ that \ form \ a \ triangle$

Answer 2

4,7,13 and 3,6,6 are line segments that cannot form a triangle