Question
Lisa has three hog panels. Panel A is 6 feet long, panel B is 8 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, 8 - 3 > 6
B.
no, 8 - 6 < 3
C.
yes, 6 + 3 > 8
D.
no, 6 + 3 < 8
A.
yes, 8 - 3 > 6
B.
no, 8 - 6 < 3
C.
yes, 6 + 3 > 8
D.
no, 6 + 3 < 8
Answers
GPT-4o mini
To determine if Lisa can create a triangular pen using the three hog panels, we need to validate the triangle inequality theorem. This theorem states that for any three sides to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Here are the lengths of the panels:
- Panel A = 6 feet
- Panel B = 8 feet
- Panel C = 3 feet
Now we check the three conditions of the triangle inequality:
1. \( A + B > C \)
\( 6 + 8 > 3 \)
\( 14 > 3 \) (True)
2. \( A + C > B \)
\( 6 + 3 > 8 \)
\( 9 > 8 \) (True)
3. \( B + C > A \)
\( 8 + 3 > 6 \)
\( 11 > 6 \) (True)
All three conditions of the triangle inequality are satisfied.
Thus the answer is **A. yes, 8 - 3 > 6**, but since it's implied through the triangle inequality, a clear choice would be option **C. yes, 6 + 3 > 8** as it directly validates the triangle inequality aspect. Therefore, it is possible for Lisa to build a triangular pen using the panels.
Here are the lengths of the panels:
- Panel A = 6 feet
- Panel B = 8 feet
- Panel C = 3 feet
Now we check the three conditions of the triangle inequality:
1. \( A + B > C \)
\( 6 + 8 > 3 \)
\( 14 > 3 \) (True)
2. \( A + C > B \)
\( 6 + 3 > 8 \)
\( 9 > 8 \) (True)
3. \( B + C > A \)
\( 8 + 3 > 6 \)
\( 11 > 6 \) (True)
All three conditions of the triangle inequality are satisfied.
Thus the answer is **A. yes, 8 - 3 > 6**, but since it's implied through the triangle inequality, a clear choice would be option **C. yes, 6 + 3 > 8** as it directly validates the triangle inequality aspect. Therefore, it is possible for Lisa to build a triangular pen using the panels.