Question

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

Answer 1

C?

Explanation:

Answer 2

Correct choice is C

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<10=b,`

these side lengths couldn't create triangle.

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

`a+b=5+7=12<13=c,`

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<10=a,`

these side lengths couldn't create triangle.