MATHEMATICS HIGH SCHOOL

What is the range of possible sizes for side x? it is a triangle with one side having 4.0, and the other having 5.6. picture attached below, thanks in advance :)

Answers

Answer 1

Answer:

Given:

Given that the two sides of the triangle are x, 4.0 and 5.6

We need to determine the range of possible sizes for the side x.

Range of x:

The range of x can be determined using the triangle inequality theorem.

The triangle inequality theorem states that, "if any side of a triangle must be shorter than the other two sides added together".

Thus, applying the theorem, we have;

$x=4.0+5.6$

$x=9.6$

Also, the the triangle inequality theorem states that, "the third side must be also larger than the difference between the other two sides".

Thus, we have;

$x=5.6-4.0$

$x=1.6$

Thus, the range of possible values for x are $1.6<x<9.6$

Answer 2

Answer:

Final answer:

In accordance with the triangle inequality theorem, the range for the length of the third side (x) in a triangle with sides of 4.0 and 5.6 is greater than 1.6 but less than 9.6.

Explanation:

In the field of Mathematics, specifically geometry, to find the range of possible lengths of a side of a triangle, you need to understand the triangle inequality theorem. The triangle inequality theorem states that the length of a side of a triangle must be less than the sum of the lengths of the other two sides, but more than the absolute difference.

Given you have two sides, 4.0 and 5.6, the possible length for side x should be less than (4.0 + 5.6 = 9.6) and greater than the absolute difference (5.6 - 4.0 = 1.6). So, the range for side x should be 1.6 < x < 9.6.

Learn more about Triangle Inequality Theorem

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Answers

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