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A triangle has two sides of lengths 4 and 15. What value could the length of
the third side be? Check all that apply

A triangle has two sides of lengths 4 and 15 What value could the length of the third side be Check all that apply class=

Respuesta :

Answer:

B, C, E

Step-by-step explanation:

The third side x could be between the limits

difference < x < sum, that is

15 - 4 < x < 15 + 4

11 < x < 19

The third side is between 11 and 19 but not 11 or 19, thus side could be

15 → B

12 → C

13 → E

After applying triangle inequality theorem, the possible values of x are

A.) 19

B.) 15

C.) 12

E.) 13

F.) 11

What is triangle inequality theorem?

Triangle inequality, in Euclidean geometry, theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.

Given the two sides of triangle as 4 and 15.

Let the third side be x.

We know that sum of two sides of a triangle should be greater than the third side.

First,

4 + x >= 15

x > = 11

Second,

15 + x >= 4

True for all possible values of x.

Third,

4 + 15 >= x

x <= 19

Implies that, 11 <= x <= 19.

Possible values of x are 19, 15, 12, 13 and 11.

Learn more about triangle inequality theorem here

https://brainly.com/question/1163433

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