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
[tex]a+b>c,\\ \\a+c>b,\\ \\b+c>a.[/tex]
A. Consider lengths a=5, b=10 and c=4. Since
[tex]a+c=5+4=9<10=b,[/tex]
these side lengths couldn't create triangle.
B. Consider lengths a=5, b=7 and c=13. Since
[tex]a+b=5+7=12<13=c,[/tex]
these side lengths couldn't create triangle.
C. Consider lengths a=7, b=9 and c=3. Since
[tex]a+b=7+9=16>3=c,\\ \\a+c=7+3=10>9=b,\\ \\b+c=9+3=12>7=a.[/tex]
These side lengths could form a triangle.
D. Consider lengths a=10, b=4 and c=5. Since
[tex]b+c=4+5=9<10=a,[/tex]
these side lengths couldn't create triangle.
