Question

Marquise finds a spare beam that is 4 feet in length.vExplain whether or not he can use these three beams to form a single triangle.

Answer 1

To determine whether Marquise can use the three beams to form a triangle, we must check the triangle inequality theorem. The theorem states that for any three lengths \(a\), \(b\), and \(c\) to form a triangle, the following conditions must be satisfied:

1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)

In this case, you mentioned that Marquise has a spare beam that is 4 feet long. However, you didn't provide the lengths of the other two beams. Let's denote the lengths of the three beams as \(a\) (4 feet), \(b\), and \(c\) (where \(b\) and \(c\) are the lengths of the other two beams).

To determine if Marquise can form a triangle, substitute the lengths into the triangle inequality conditions:

- \(4 + b > c\)
- \(4 + c > b\)
- \(b + c > 4\)

If all of these inequalities hold true when specific values for \(b\) and \(c\) are provided, then Marquise can use the three beams to form a triangle. If any of the conditions fail, then he cannot.

Please provide the lengths of the other two beams (b and c) to make a conclusive determination.