Question

The measure of two sides of a triangle are 7 and 11. Determine the range of values for the third side of the triangle.(1 point)
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Answer 1

The measures of two sides of a triangle are 5.2 and 8.1. Determine the range of values for the third side of the triangle.(1 point)
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Answer 2

To determine the range of values for the third side of a triangle, we need to apply the triangle inequality theorem.

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.

In this case, let's assume the third side of the triangle has a length of x. According to the triangle inequality theorem, we have two inequalities:

7 + 11 > x
11 + x > 7

Simplifying these inequalities, we have:

18 > x
11 + x > 7

To find the range of values for x, we need to solve these inequalities.

From the first inequality, we have:
x < 18

From the second inequality, we have:
x > -4

So, the range of values for the third side of the triangle is -4 < x < 18.

Answer 3

To determine the range of values for the third side of the triangle, we can apply the triangle inequality theorem.

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.

Let's assume the third side of the triangle has a length of x. According to the triangle inequality theorem, we have two inequalities:

5.2 + 8.1 > x
8.1 + x > 5.2

Simplifying these inequalities, we have:

13.3 > x
8.1 + x > 5.2

From the first inequality, we have:
x < 13.3

From the second inequality, we have:
x > -2.9

So, the range of values for the third side of the triangle is -2.9 < x < 13.3.