Question

Kevin is making a wooden frame in the shape of a triangle. He has pieces of wood of lengths 8 inches and 15 inches. Which of the following lengths of wood could Kevin use to complete the frame?

Answer 1

Kevin could use pieces of wood with lengths 8, 8, and 15 inches to complete the frame.

Step-by-step explanation:

To complete the frame, Kevin needs to use pieces of wood that satisfy the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, if a, b, and c are the lengths of the sides of a triangle, then a + b > c, a + c > b, and b + c > a.

In this case, Kevin has pieces of wood with lengths 8 inches and 15 inches. Let's check which of the given lengths could complete the frame:

1. 
   
3. 8 + 8 = 16, which is greater than 15 and satisfies the theorem.
4. 
   
6. 8 + 15 = 23, which is greater than 8 and satisfies the theorem.
7. 
   
9. 15 + 15 = 30, which is greater than 8 and satisfies the theorem.

Therefore, Kevin could use pieces of wood with lengths 8, 8, and 15 inches to complete the frame.

Learn more about Triangle inequality theorem