Question

Find the range and values for the third side of the triangle, x, based on the diagram.

2 of the sides are measured as 7.

Answer 1

To determine the range and values for the third side of the triangle, you can use the Triangle Inequality Theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side.

Given that two sides of the triangle are measured as 7, let's say those sides are a and b. Without loss of generality, we can assume that a = 7 and b = 7.

Applying the Triangle Inequality Theorem, we have the following inequality:

7 + 7 > x

Simplifying the inequality, we get:

14 > x

Therefore, the range for the third side of the triangle, x, is x < 14.

In other words, the third side must be less than 14 units in order for a triangle to be formed.

As for the values, any length less than 14 can be a possible value for x, as long as it satisfies the condition of being the length of the third side of a triangle with the given side lengths.