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 \( b \):
- \( a + b > c \) (i.e., \( a + b > 4 \))
- \( a + c > b \) (i.e., \( a + 4 > b \))
- \( b + c > a \) (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.