What is the minimum side length needed to complete the triangle? Explain.
The side length needed to complete the triangle must be ___ inch(es) long. (Type a whole number.)
greater than
equal to
less than
What is the minimum side length needed to complete the triangle? Explain
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To determine the minimum side length needed to complete a triangle, you can 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.
If you have two sides of the triangle, let’s call them a and b, and you want to find the minimum length c needed for the third side, the following must hold true:
1. a + b > c
2. a + c > b
3. b + c > a
From these, the minimum length for c can be calculated using the first inequality:
c must be less than the sum of a and b.
For instance, if you know the lengths of sides a and b are 3 inches and 4 inches, you’ll calculate:
c must be < (3 + 4) = 7 inches.
So, in this case, the side length needed to complete the triangle must be less than 7 inches.
The side length needed to complete the triangle must be less than ___ inch(es) long.
If you provide the lengths of the two known sides, I can help you find the specific answer!