Question
Which of the following statements about side lengths of a triangle is valid? Sides with lengths 5,13. and 13 centimeters can form a triangle. Sides with lengths 2, 3 and 6 centimeters can form a triangle Sides with lengths 113.and 27 centimeters can form a triangle Sides with lengths 2. 12. and 16 centimeters can form a triangle
Solution
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WyattElite · Tutor for 8 years
Answer
### Sides with lengths 5, 13, and 13 centimeters can form a triangle.
Explain
## Step 1: Triangle Inequality Theorem
### The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This is known as the Triangle Inequality Theorem.
## Step 2: Check Option 1 (5, 13, 13)
### 5 + 13 > 13
## Step 3: Check Option 2 (2, 3, 6)
### 2 + 3 = 5 < 6
## Step 4: Check Option 3 (1, 13, 27)
### 1 + 13 = 14 < 27
## Step 5: Check Option 4 (2, 12, 16)
### 2 + 12 = 14 < 16
### The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This is known as the Triangle Inequality Theorem.
## Step 2: Check Option 1 (5, 13, 13)
### 5 + 13 > 13
, 13 + 13 > 5
, and 5 + 13 > 13
. All conditions are met.
## Step 3: Check Option 2 (2, 3, 6)
### 2 + 3 = 5 < 6
. This violates the Triangle Inequality Theorem.
## Step 4: Check Option 3 (1, 13, 27)
### 1 + 13 = 14 < 27
. This violates the Triangle Inequality Theorem.
## Step 5: Check Option 4 (2, 12, 16)
### 2 + 12 = 14 < 16
. This violates the Triangle Inequality Theorem.
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