Question

Angela has three hog panels. Panel A is 8 feet long, panel B is 9 feet long, and panel C is 3 feet long. If the full length of each panel is used, can she build a triangular pen to hold her pet pig?
A.
yes, 9 - 3 > 8
B.
yes, 8 + 3 > 9
C.
no, 8 + 3 < 9
D.
no, 9 - 8 < 3

Answer 1

To determine if Angela can build a triangular pen with the given panels, we must apply the triangle inequality theorem. According to this theorem, for any triangle with sides of lengths \(a\), \(b\), and \(c\), the following conditions must hold:

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

Let’s assign the lengths to the panels:
- \(a = 8\) feet (Panel A)
- \(b = 9\) feet (Panel B)
- \(c = 3\) feet (Panel C)

Now, we will check the three inequalities:

1. **Check \(a + b > c\):**
\(8 + 9 > 3\)
\(17 > 3\) (True)

2. **Check \(a + c > b\):**
\(8 + 3 > 9\)
\(11 > 9\) (True)

3. **Check \(b + c > a\):**
\(9 + 3 > 8\)
\(12 > 8\) (True)

Since all three inequalities are satisfied, Angela can indeed build a triangular pen with the three panels.

The correct answer is **A. yes, 9 - 3 > 8**.