Apply the triangle Inequality Theorem and determine which option could be the third side of a triangle if the first two sides measure 4 and 6

Question

A.11
B.9
C.2
D.1

Answer 1

To determine if a given length could be the third side of a triangle, we apply the Triangle Inequality Theorem.

According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given sides of lengths 4 and 6, we need to check if the options satisfy this condition:

A. 11
4 + 6 > 11
10 > 11
This is not true, so 11 cannot be the third side of the triangle.

B. 9
4 + 6 > 9
10 > 9
This is true, so 9 could be the third side of the triangle.

C. 2
4 + 6 > 2
10 > 2
This is true, so 2 could be the third side of the triangle.

D. 1
4 + 6 > 1
10 > 1
This is true, so 1 could be the third side of the triangle.

Therefore, options B, C, and D could be the third side of a triangle with the first two sides measuring 4 and 6.