Question

For each set of three measures, indicate which ones could be the sides of a triangle. (Note: the triangle does not need to be a right triangle.) A) 7, 9, 16 B) 15, 16, 30 C) 6.5, 9.5, 16.5 D) 8, 12, 24.8

Answer 1

From the given sets, only set B with the measures 15, 16, 30 can form a triangle. This is determined using the triangle inequality theorem, which states the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step-by-step explanation:

In Mathematics, the triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. We can apply this theorem to check which of the given sets can make a triangle.

• For A) 7, 9, 16, 7+9=16 which is equal to the third side, not greater, so it cannot form a triangle.
• For B) 15, 16, 30, 15+16=31 which is more than the third side, so this can form a triangle.
• For C) 6.5, 9.5, 16.5, 6.5+9.5 = 16 which is less than the third side, so it can't form a triangle.
• For D) 8, 12, 24.8, 8+12 = 20 which is less than the third side, so it can't form a triangle.

Learn more about Triangle Inequality Theorem