Question

Determine the possible range of x (the value of the third side of a triangle) if the two side lengths given are 5 and 12.

a) x can be any real number
b) x must be greater than 7 but less than 17
c) x must be greater than 17
d) x must be less than 7

Answer 1

The third side x of a triangle with sides of length 5 and 12 must be greater than 7 and less than 17 according to the Triangle Inequality Theorem.

Step-by-step explanation:

To find the range of possible values for the third side x of a triangle when given two sides of lengths 5 and 12, we must apply the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Therefore, we have two inequalities:

1. 5 + 12 > x, which simplifies to 17 > x.
2. 12 + x > 5 and 5 + x > 12, which simplify to x > 7 (from the second inequality).

To satisfy both conditions simultaneously, the value of x must be greater than 7 but less than 17.

Therefore, the correct answer is:

b) x must be greater than 7 but less than 17.