Question

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

Answer 1

To determine if Marquise can use the three beams to form a triangle, we can apply the triangle inequality theorem. This theorem states that for any three sides of a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let's denote the lengths of the three beams:
- First beam: \( a \)
- Second beam: \( b \)
- Third beam: \( c = 4 \) feet (the spare beam)

To provide a conclusive answer, we need the lengths of the other two beams. However, if we only have the spare beam's length, we can still illustrate the process:

Assuming the lengths of the other beams are \( a \) and \( b \):
1. \( a + b > c \) (i.e., \( a + b > 4 \))
2. \( a + c > b \) (i.e., \( a + 4 > b \))
3. \( b + c > a \) (i.e., \( b + 4 > a \))

If Marquise can find values for \( a \) and \( b \) that satisfy all three inequalities, then he can indeed form a triangle. Without knowing the lengths of the other two beams, we cannot definitively say whether he can or cannot form a triangle.

If you can provide the lengths of the other two beams, we can further evaluate this.