Samantha has three hog panels. Panel A is 3 feet long, panel B is 7 feet long, and panel C is 9 feet long. If the full length of each panel is used, can she build a triangular pen to hold her pet pig?

Question

A.
yes, 3 + 7 > 9
B.
yes, 9 - 3 > 7
C.
no, 3 + 7 < 9
D.
no, 9 - 7 < 3

Answer 1

To determine if Samantha can create a triangular pen with the given panels A, B, and C, we can use the triangle inequality theorem. This theorem states that for any three lengths to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

The lengths of the panels are:

• Panel A: 3 feet
• Panel B: 7 feet
• Panel C: 9 feet

Now, we will check the conditions of the triangle inequality:

1. 3 + 7 > 9 (A + B > C)

   • 3 + 7 = 10, and 10 > 9, which is true.

2. 3 + 9 > 7 (A + C > B)

   • 3 + 9 = 12, and 12 > 7, which is true.

3. 7 + 9 > 3 (B + C > A)

   • 7 + 9 = 16, and 16 > 3, which is also true.

Since the first condition fails (3 + 7 is not greater than 9), we can conclude:

C. no, 3 + 7 < 9

Thus, the correct answer is C.