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.

1 answer

To determine if Marquise can use the three beams to form a triangle, we need to apply 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, we only know one length, which is 4 feet. We need the lengths of the other two beams to make a determination. Assuming you have the lengths of the other two beams, you can apply the triangle inequality theorem as follows:

  1. Let’s say the lengths of the other two beams are \(x\) and \(y\).
  2. Check the inequalities:
    • \(4 + x > y\)
    • \(4 + y > x\)
    • \(x + y > 4\)

If all three conditions hold true, then the beams can form a triangle. If even one condition does not hold, then it’s not possible to form a triangle with those lengths.

Please provide the lengths of the other two beams for a more detailed analysis.