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A triangle has side lengths measuring 3x cm, 7x cm, and h cm. Which expression describes the possible values of h, in cm? 4x < h < 10x 10x < h < 4x h = 4x h = 10x

Respuesta :

calculista

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

so

Three conditions mus be satisfied

Condition N [tex]1[/tex]

[tex]3x+7x > h\\ 10x > h\\h< 10x[/tex]

Condition N [tex]2[/tex]

[tex]3x+h > 7x\\ h > 7x-3x\\h> 4x[/tex]

Condition N [tex]3[/tex]

[tex]7x+h > 3x\\ h > 3x-7x\\h> -4x[/tex] (condition N 3 is included in condition N 2)

therefore

[tex]h> 4x\\ h< 10x\\ 4x < h < 10x[/tex]

the answer is the option

4x < h < 10x



facundo3141592

The possible values of the third side of the triangle are given by the inequality:

10x > h > 4x

How to find the possible lengths of the missing side?

For a triangle of sides a, b, and c, the triangle inequality theorem says that the sum of any two sides must be larger than the other side. So we must have:

  • a + b > c
  • a + c > b
  • b + c > a

In this case, we have the sides:

3x , 7x, and h.

Then we must have:

  • 3x + 7x > h
  • 3x + h > 7x
  • 7x + h > 3x

Solving all of these for h, we get:

3x + 7x > h

h > 7x - 3x  

h > 3x - 7x

The third one gives a negative value, so we can discard that one, using the first and the second one we get:

3x + 7x > h > 7x - 3x

10x > h > 4x

This inequality gives all the possible values of h.

If you want to learn more about triangles, you can read:

https://brainly.com/question/21442022

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