Li-Hua wants to create a triangular fame. She has two pieces of wood, which are 6 inches long and 9 inches long, to use for two sides of the triangle. Which of the following CANNOT be the lenth of the third frame and why?

a) 4 inches
b) 6 inches
c) 13 inches
d) 16 inches

in a triangle, the sum of any two sides must be greater than the third side. so ....

So, D? 16

To determine which of the following lengths cannot be the length of the third side of the triangle, we can use 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.

Now let's check each option:

a) 4 inches: In this case, the sum of the two given sides (6 inches and 9 inches) would be 6 + 9 = 15 inches, which is greater than 4 inches. So, a triangle with sides measuring 6, 9, and 4 inches can be formed.

b) 6 inches: Again, the sum of the given sides (6 inches and 9 inches) is 6 + 9 = 15 inches, which is equal to the third side. This means it is a degenerate triangle, where the three sides lie on a straight line. So, a triangle with sides measuring 6, 9, and 6 inches cannot be formed.

c) 13 inches: The sum of the given sides (6 inches and 9 inches) is 6 + 9 = 15 inches, which is less than 13 inches. Therefore, a triangle with sides measuring 6, 9, and 13 inches cannot be formed.

d) 16 inches: Once again, the sum of the given sides (6 inches and 9 inches) is 6 + 9 = 15 inches, which is less than 16 inches. Hence, a triangle with sides measuring 6, 9, and 16 inches cannot be formed.

To conclude, the answer is (c) 13 inches.