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)

Question

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Answer 1

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

According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

So for this triangle with sides of 7 and 11, we can set up the following inequalities:
7 + 11 > x
11 + x > 7
7 + x > 11

Solving these inequalities, we get:
18 > x
x > -4
x > 4

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

Answer 2

now do this

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 3

To determine the range of values for the third side of the triangle with sides of 5.2 and 8.1, we can use the triangle inequality theorem.

According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

So for this triangle with sides of 5.2 and 8.1, we can set up the following inequalities:
5.2 + 8.1 > x
8.1 + x > 5.2
5.2 + x > 8.1

Solving these inequalities, we get:
13.3 > x
x > -2.9
x > 2.9

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