Question

What is the range of possible sizes for side x?

Answer 1

Explanation:

to be a real triangle every side must be shorter than the sum of the other 2 sides.

so,

x < 2.7 + 4.0 = 6.7

4.0 < 2.7 + x

1.3 < x

2.7 < 4.0 + x

-1.3 < x

the negative constraint does not apply for a side length.

so, we get

1.3 < x < 6.7

Answer 2

Without additional context, I assume you're referring to the sides of a triangle. In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem.

Given side 1 = 2.7 and side 2 = 4.0, let's consider side x:

For the triangle inequality to hold, we have two inequalities:

1. x + 2.7 > 4.0

2. x + 4.0 > 2.7

Solving these inequalities:

1. x > 4.0 - 2.7

x > 1.3

2. x > 2.7 - 4.0

x > -1.3

Combining these results, the range of possible sizes for side x is x > 1.3 (since negative side lengths aren't meaningful in this context).

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