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 7 inches. which could be the length in inches of the third piece of string dino used?
A) 2
B) 8
C) 5****
D) 3
7-3 < x < 7+3
4 < x < 10
So, B or C looks good
To determine the length of the third piece of string that Dino used, we need to apply 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.
Let's check each option:
A) If the length of the third piece is 2 inches, then the sum of the lengths of the other two pieces (3 inches and 7 inches) is 10 inches. Since 10 is greater than 2, this option satisfies the triangle inequality theorem.
B) If the length of the third piece is 8 inches, then the sum of the lengths of the other two pieces (3 inches and 7 inches) is 10 inches. Since 10 is equal to 8, this option does not satisfy the triangle inequality theorem.
C) If the length of the third piece is 5 inches, then the sum of the lengths of the other two pieces (3 inches and 7 inches) is 10 inches. Since 10 is equal to 5, this option does not satisfy the triangle inequality theorem.
D) If the length of the third piece is 3 inches, then the sum of the lengths of the other two pieces (3 inches and 7 inches) is 10 inches. Since 10 is equal to 3, this option does not satisfy the triangle inequality theorem.
Based on the triangle inequality theorem, option C (5 inches) could be the length of the third piece of string that Dino used.