# Can the sides of a triangle have lengths 8, 13, and 20?

## Answers

yes but not if those numbers are the sides

Step-by-step explanation:

yes

Step-by-step explanation:

The sum of any two sides of triangle should be more than the third side.

8 + 13 = 21 > 20

13+20 = 33 > 8

8 + 20 = 28 > 13

1. You have that two sides of a triangle have lengths of 6 and 13. Then, by the Triangle Inequality Theorem, you have:

a+b>c

a+c>b

b+c>a

3. Therefore, you have:

a=6

b=13

c<a+b

c<6+13

c<19

4. The difference between a and b should be lesser that c. Then

a-b<c

13-6<c

7<c

5. Therefore:

c=x

7<x<19

The correct answer is the option B: B. 7<x<19

4. 4, 8, 11 could be the lengths of the sides of a triangle

5. 6, 12, 5 could not be the lengths of the sides of a triangle

6. 13, 13, 26 could not be the lengths of the sides of a triangle

Step-by-step explanation:

There is an important rule about the sides of the triangle

The sum of lengths of the smallest two sides of a triangle must be greater than the length of the third sideLet us use this rule to solve questions 4, 5, and 6

#4.

∵ The numbers are 4, 8, 11

∵ The two smallest numbers are 4, 8

∵ Their sum = 4 + 8 = 12

∵ The greatest number is 11

∵ 12 > 11

∴ The sum of the two smallest number is greater than the third number

∴ The numbers could be the length of the sides of a triangle

∴ 4, 8, 11 could be the lengths of the sides of a triangle

#5.

∵ The numbers are 6, 12, 5

∵ The two smallest numbers are 5, 6

∵ Their sum = 5 + 6 = 11

∵ The greatest number is 12

∵ 11 < 12

∴ The sum of the two smallest number is smaller than the third number

∴ The numbers could not be the length of the sides of a triangle

∴ 6, 12, 5 could not be the lengths of the sides of a triangle

#6.

∵ The numbers are 13, 13, 26

∵ The two smallest numbers are 13, 13

∵ Their sum = 13 + 13 = 26

∵ The greatest number is 26

∵ 26 = 26

∴ The sum of the two smallest number is equal to the third number

∴ The numbers could not be the length of the sides of a triangle

∴ 13, 13, 26 could not be the lengths of the sides of a triangle

Answerjust add three of the numbers until you get 13

Step-by-step explanation:

B

Step-by-step explanation:

By using the Triangle Inequality Theorem, we can say that the third side will be in between the SUM of the other two sides and DIfference of the other two sides.

The other 2 sides given lengths are 6 & 13.

Sum of 6 and 13 is 6 + 13 = 19, and

Difference of 13 and 6 is 13 - 6 = 7

Hence, the 3rd side will be between 7 and 19

Or, 7 < x < 19, answer choice B

The answer is B

Step-by-step explanation:

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They all can because they all have 3 lengths, is there a picture to go with it?

Step-by-step explanation:

Triangle 1

Step-by-step explanation:

Triangle 1 is a right triangle

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A can’t because the 13 throws it off