By The triangle inequality theorem and which set of side lengths could create a triangle? A 5, 10, 4. B. 5, 7, 13. C. 7,9,3. D.

Question

tester [92]

3 years ago

10

By The triangle inequality theorem and which set of side lengths could create a triangle? A 5, 10, 4. B. 5, 7, 13. C. 7,9,3. D.

10,4,5

Mathematics

2 answers:

Yuri [45] · Answer 1 · 2022-06-30T23:01:59+03:00

Answer:

Correct choice is C

Step-by-step explanation:

Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. Thus, if a, b and c are triangles sides, then

$a+b>c,\\ \\a+c>b,\\ \\b+c>a.$

A. Consider lengths a=5, b=10 and c=4. Since

$a+c=5+4=9$

these side lengths couldn't create triangle.

B. Consider lengths a=5, b=7 and c=13. Since

$a+b=5+7=12$

these side lengths couldn't create triangle.

C. Consider lengths a=7, b=9 and c=3. Since

$a+b=7+9=16>3=c,\\ \\a+c=7+3=10>9=b,\\ \\b+c=9+3=12>7=a.$

These side lengths could form a triangle.

D. Consider lengths a=10, b=4 and c=5. Since

$b+c=4+5=9$

these side lengths couldn't create triangle.

Illusion [34] · Answer 2 · 2022-07-01T01:30:57+03:00

Illusion [34]3 years ago

3 0

Answer:

C?

Step-by-step explanation: