Question

Triangle Properties: Mastery Test

Select all the correct answers.
Claire, Amy, and Becky are at an art show. They are currently looking at different pieces of art. Claire is standing 6 feet from Amy and 15 feet from
Becky. Which of the following three values represent possible lengths between Amy and Becky so that Amy, Becky, and Claire are standing at the
vertices of a triangle?
4 ft
20 ft
12 ft
15 ft
9 ft
Sube
24 ft

Answer 1

The lengths between Amy and Becky that can form a triangle with Claire are 12 ft, 15 ft, and 20 ft.

Step-by-step explanation:

In order for Amy, Becky, and Claire to form a triangle, the lengths of the sides must 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. Let's analyze the given information:

• Claire is standing 6 feet from Amy and 15 feet from Becky.
• In a triangle, the sum of the two shorter sides must be greater than the longest side.
• If 12 feet is the length between Amy and Becky, then 6+12=18, which is greater than 15. So 12 feet is a possible length.
• If 15 feet is the length between Amy and Becky, then 6+15=21, which is greater than 15. So 15 feet is a possible length.
• If 9 feet is the length between Amy and Becky, then 6+9=15, which is NOT greater than 15. So 9 feet is NOT a possible length.
• If 4 feet is the length between Amy and Becky, then 6+4=10, which is NOT greater than 15. So 4 feet is NOT a possible length.
• If 20 feet is the length between Amy and Becky, then 6+20=26, which is greater than 15. So 20 feet is a possible length.

Therefore, the correct answer is: 12 ft, 15 ft, and 20 ft.