Question

6) Find the range of values for x using the

Triangle Inequality Theorem.
X
15.4
7.6

Answer 1

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Using this theorem, we can find the range of values for x in the given triangle:

x + 7.6 > 15.4
x > 7.8

x + 15.4 > 7.6
x > -7.8

Therefore, the range of values for x is:

7.8 < x < 7.8

Answer 2

Given two known side lengths of 7.6 units and 15.4 units, we can apply the Triangle Inequality Theorem to determine the range of values for the missing side length, x, Therefore, the range of values for x is -7.8 < x < 23.

Analyzing the provided image, we can identify a triangle with two known side lengths, 7.6 units and 15.4 units. The task is to determine the range of values for the missing side length, represented by the variable x. To achieve this, we'll employ the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the measure of the remaining side.

Applying the theorem, we have the following inequalities:

1. 7.6 + x > 15.4

2. x + 15.4 > 7.6

3. 7.6 + 15.4 > x

Solving these inequalities separately, we get:

1. x > 7.8

2. x > -7.8

3. 23 > x

Combining these results, we can deduce that the range of values for x is:

x > -7.8 (so x ≥ -7.8)

7.8 < x < 23 (so -7.8 < x < 23)

Therefore, the missing side length, represented by x, lies between -7.8 units and 23 units.

Complete question below:

Find the range of values for x using theTriangle Inequality Theorem For the given figure below.