Dino used three pieces of string to make a model of a triangle in art class. The lengths of two of the pieces of string were 3 inches and 8 inches. Which could be the length in inches of the third piece of string Dino used?
A)2
B)8
C)5
D)3
I think D?
Use this:
(8-3) < x < (8+3)
"x" as the third piece.
Check your answer again.
It must be longer than 5 which is 8-3
It must be shorter than 11 which is 8+3
To find the possible length of the third piece of string, we need to apply the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's consider the given lengths: 3 inches and 8 inches.
To find the possible length of the third side, we need to check if the sum of each pair of given sides is greater than the third side.
Pair 1: 3 inches + 8 inches = 11 inches
Pair 2: 3 inches + X inches (third side) should be greater than X inches.
Pair 3: 8 inches + X inches (third side) should be greater than X inches.
From the pairs above, we can see that the third side length should be greater than the difference between the sum of the two given sides and 8 inches.
Pair 1: 11 inches - 8 inches = 3 inches
Pair 2: 3 inches < X (third side)
Pair 3: 8 inches < X (third side)
Therefore, the possible length of the third piece of string Dino used could be greater than 3 inches. Thus, option D) 3 is not a valid answer.
The remaining possible lengths are:
A) 2 inches
B) 8 inches
C) 5 inches
Without knowing the specific lengths of all three pieces, we cannot determine the exact length of the third piece. However, based on the triangle inequality theorem, it is possible for the third piece of string to have a length of either 2 inches (option A) or 5 inches (option C).