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m_a_m_a [10]
3 years ago
14

What is the range of possible sizes for side x

Mathematics
1 answer:
Xelga [282]3 years ago
3 0

Answer:

0.5 < x < 16.5

Step-by-step explanation:

For a triangle (by the triangular inequality theorem), we know that the sum of any two sides must be larger than the other side.

When we have a triangle and we know two sides, let's define the measures of these sides as S1 and S2.   (such that S2 > S1)

By the first property, we will have that S1 + S2 > S3

Where S3 is the third side, the one that we do not know.

But there is also a lower restriction, given by:

S2 - S1 < S3 < S1 + S2

This is because we also must have:

S1 + S3 > S2

and

S2 + S3 > S1

We can rewrite both of these to get:

S2 - S1 < S3

S1 - S2 < S3

Because S2 > S1, the first inequality is more restrictive, so we need to use that one.

Then we get the inequality:

S2 - S1 < S3 < S1 + S2

Ok, in this case, the shorter side is 8.0 then:

S1 = 8.0

And the longer side is 8.5, then:

S2 = 8.5

And the third side is x, S3 = x

Replacing those in our inequality, we get:

8.5 - 8.0 < x < 8.5 + 8.0

0.5 < x < 16.5

This is the range of possible sizes for side x.

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The hypotenuse of a right triangle is the side opposite the right angle. It is the longest side of a right triangle. There is only one hypotenuse in a triangle, so there is no confusion with the hypotenuse.

The two sides that form the right angle are called the legs. Each leg is opposite an acute angle. The legs may or may not be congruent to each other, but each leg is always shorter than the hypotenuse. Since there are two legs, we need to be able to distinguish them. If you take an acute angle as your angle of interest, the leg that is part of the angle is called the adjacent leg. The other leg is the opposite leg. Adjacent leg and opposite leg are relative terms. They depend on the acute angle you are considering.

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