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Which of the following sets of lengths can be used to form the sides of a triangle? Explain your reasoning. 5 inches, 8 inches, 20 inches 3 inches, 16 inches, 18 inches 2 inches, 5 inches, 7 inches

User Cmcginty
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1 Answer

2 votes

Answer:

3 inches, 16 inches, 18 inches

Explanation:

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

Verify each case

case 1) we have

5 inches, 8 inches, 20 inches

Applying the triangle Inequality Theorem

1) 5+8 > 20

13 > 20 ------> is not true

therefore

The set of lengths cannot be used to form the sides of a triangle

case 2) we have

3 inches, 16 inches, 18 inches

Applying the triangle Inequality Theorem

1) 3+16 > 18

19 > 18 ------> is true

2) 3+18> 16

21 > 16 -----> is true

3) 16+18 > 3

34 > 3 -----> is true

therefore

The set of lengths can be used to form the sides of a triangle

case 3) we have

2 inches, 5 inches, 7 inches

Applying the triangle Inequality Theorem

1) 2+5 > 7

7 > 7 ------> is not true

therefore

The set of lengths cannot be used to form the sides of a triangle

User Alejandro Arbiza
by
5.6k points
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