Question

use the image to answer the question.
find the range of values for the third side of the triangle, x, based on the diagram.
(1 point)

Explanation:

Step1: Identify triangle type

It's an isosceles triangle with two sides = 7.

Step2: Apply triangle inequality

For a triangle, the sum of two sides > third side, and the difference of two sides < third side.
So, \( 7 - 7 < x < 7 + 7 \)

Step3: Simplify the inequality

\( 0 < x < 14 \) (but since length can't be 0, and it's a triangle, \( x > 0 \) and \( x < 14 \), but more precisely, as a valid triangle, \( 0 < x < 14 \), but since it's a triangle with two sides 7, \( x \) must be greater than 0 and less than 14, but in context, \( 0 < x < 14 \), but actually, the strict inequality from triangle inequality: \( |7 - 7| < x < 7 + 7 \), so \( 0 < x < 14 \). But since a triangle can't have a side of length 0, the range is \( 0 < x < 14 \), but more accurately, for a non - degenerate triangle, the third side must be greater than 0 and less than the sum of the other two sides. Since the other two sides are both 7, the sum is 14 and the difference is 0. So the range is \( 0 < x < 14 \), but in the context of a triangle (non - degenerate), \( x \) must satisfy \( 0 < x < 14 \). However, since the triangle has two sides of length 7, the third side \( x \) must be greater than 0 and less than 14. But usually, we write it as \( 0 < x < 14 \), but more precisely, using the triangle inequality theorem: the length of any side of a triangle must be greater than the absolute difference of the other two sides and less than the sum of the other two sides. So \( |7 - 7| < x < 7+7 \), which simplifies to \( 0 < x < 14 \).

Answer:

The range of values for \( x \) is \( 0 < x < 14 \)