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In Mathematics / High School | 2014-03-26

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

A. 6 cm, 8 cm, 10 cm
B. 5 cm, 6 cm, 7 cm
C. 4 cm, 7 cm, 13 cm
D. 3 cm, 6 cm, 6 cm

Asked by necse

Answer (3)

T o b u i l d a t r ian g l e w i t h t h ese se g m e n t s , m u s t b e t h e co n d i t i o n :
c \\ a+c>b \\ b+c>a"> a + b > c a + c > b b + c > a
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 = 6 c m , b = 8 c m , c = 10 c m 6 c m + 8 c m > 10 c m 6 c m + 10 c m > 8 c m 8 c m + 10 c m > 6 c m 14 c m > 10 c m 16 c m > 8 c m 18 c m > 6 c m a re l in e se g m e n t s t ha t f or m a t r ian g l e
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 = 5 c m , b = 6 c m , c = 7 c m 5 c m + 6 c m > 7 c m 5 c m + 7 c m > 6 c m 6 c m + 7 c m > 5 c m 11 c m > 7 c m 12 c m > 6 c m 13 c m > 5 c m a re l in e se g m e n t s t ha t f or m a t r ian g l e
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 = 4 c m , b = 7 \cm , c = 13 \cm 4 c m + 7 c m > 13 c m 4 c m + 13 c m > 7 c m 7 c m + 13 c m > 4 c m 11 c m < 13 c m 17 c m > 6 c m 20 c m > 4 c m a re l in e se g m e n t s t ha t c ann o t f or m a t r ian g l e
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"> a = 3 c m , b = 6 \cm , c = 6 \cm 3 c m + 6 c m > 6 c m 3 c m + 6 c m > 6 c m 6 c m + 6 c m > 3 c m 9 c m > 6 c m 9 c m > 6 c m 12 c m > 3 c m a re l in e se g m e n t s t ha t f or m a t r ian g l e

Answered by Lilith | 2024-06-10

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

Answered by deathstrike001 | 2024-06-10

The triangle inequality theorem helps us determine that option C (4 cm, 7 cm, 13 cm) cannot form a triangle, as it fails the condition where the sum of two sides must be greater than the third side. Other options can successfully form triangles. Therefore, option C is the correct answer.
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Answered by Lilith | 2024-09-27

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