AI tutor
Welcome to Bytelearn!
Let’s check out your problem:
Given and as the lengths of two sides of a triangle, find the range of values for the third side.Enter the number that belongs in the green box. Enter International Academy of Science. All Rights Reserved.
Full solution
Q. Given and as the lengths of two sides of a triangle, find the range of values for the third side.Enter the number that belongs in the green box. Enter International Academy of Science. All Rights Reserved.
- Use Triangle Inequality Theorem: To find the range of the third side, we use the Triangle Inequality Theorem which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
- Find Minimum Length: First, let's find the minimum length of the third side. It must be greater than the difference of the other two sides.So, we calculate .
- Calculate Minimum Length: .So, the third side must be greater than .
- Find Maximum Length: Now, let's find the maximum length of the third side. It must be less than the sum of the other two sides.So, we calculate .
- Calculate Maximum Length: .So, the third side must be less than .
- Determine Range: Therefore, the range of possible lengths for the third side is greater than and less than .
More problems from Evaluate variable expressions: word problems
QuestionGet tutor help
QuestionGet tutor help
QuestionGet tutor help
QuestionGet tutor help
QuestionGet tutor help