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.](https://tex.z-dn.net/?f=a%2Bb%3Ec%2C%5C%5C%20%5C%5Ca%2Bc%3Eb%2C%5C%5C%20%5C%5Cb%2Bc%3Ea.)
A. Consider lengths a=5, b=10 and c=4. Since
![a+c=5+4=9](https://tex.z-dn.net/?f=a%2Bc%3D5%2B4%3D9%3C10%3Db%2C)
these side lengths couldn't create triangle.
B. Consider lengths a=5, b=7 and c=13. Since
![a+b=5+7=12](https://tex.z-dn.net/?f=a%2Bb%3D5%2B7%3D12%3C13%3Dc%2C)
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.](https://tex.z-dn.net/?f=a%2Bb%3D7%2B9%3D16%3E3%3Dc%2C%5C%5C%20%5C%5Ca%2Bc%3D7%2B3%3D10%3E9%3Db%2C%5C%5C%20%5C%5Cb%2Bc%3D9%2B3%3D12%3E7%3Da.)
These side lengths could form a triangle.
D. Consider lengths a=10, b=4 and c=5. Since
![b+c=4+5=9](https://tex.z-dn.net/?f=b%2Bc%3D4%2B5%3D9%3C10%3Da%2C)
these side lengths couldn't create triangle.