Answer :

matthew6211
To determine which sets of measurements could be the side lengths of a triangle, we can apply 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 remaining side.

Let's check each set of measurements:

1. \(6\, \text{cm},\, 7\, \text{cm},\, 8\, \text{cm}\)
\(6 + 7 > 8\) (True)
\(6 + 8 > 7\) (True)
\(7 + 8 > 6\) (True)
This set forms a valid triangle.

2. \(5\, \text{cm},\, 9\, \text{cm},\, 14\, \text{cm}\)
\(5 + 9 > 14\) (False)
This set cannot form a triangle.

3. \(3\, \text{cm},\, 3\, \text{cm},\, 3\, \text{cm}\)
All sides are equal, so this forms an equilateral triangle, which is valid.

4. \(4\, \text{cm},\, 8\, \text{cm},\, 13\, \text{cm}\)
\(4 + 8 > 13\) (False)
This set cannot form a triangle.

5. \(7\, \text{cm},\, 7\, \text{cm},\, 10\, \text{cm}\)
\(7 + 7 > 10\) (True)
\(7 + 10 > 7\) (True)
\(7 + 10 > 7\) (True)
This set forms a valid triangle.

So, the correct sets of measurements that could be the side lengths of a triangle are:
- \(6\, \text{cm},\, 7\, \text{cm},\, 8\, \text{cm}\)
- \(3\, \text{cm},\, 3\, \text{cm},\, 3\, \text{cm}\)
- \(7\, \text{cm},\, 7\, \text{cm},\, 10\, \text{cm}\)

Other Questions