| What to create | Quiz |
| Which subject | Mathematics |
| What age group | Year or Grade 8 |
| What topic | Contextualized assessment about triangle inequalities |
| Question types | Open-ended |
| Number of questions | 5 |
| Number of answers | 4 |
| Correct answers | Exactly 1 |
| Show correct answers | |
| Use images (descriptions) | |
| Any other preferences |
Answer each question below. Each question is related to triangle inequalities and requires you to demonstrate your understanding of the concepts.
Triangle Formation A triangle must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side. Given the side lengths 7 cm, 10 cm, and 5 cm, determine if these lengths can form a triangle. Justify your answer.
Finding a Range If one side of a triangle measures 12 cm, and the second side measures 15 cm, what is the possible range of lengths for the third side? Explain how you arrived at your answer using the triangle inequality theorem.
Real-Life Application A triangular garden has two sides measuring 8 meters and 6 meters. If the length of the third side is labeled as x, write an inequality that must be satisfied by x in order for the garden to be a valid triangle. Then, determine the range for x.
Comparative Analysis Consider three triangles with sides measuring (4 cm, 5 cm, 6 cm), (1 cm, 2 cm, 3 cm), and (3 cm, 4 cm, 5 cm). Identify which triangles satisfy the triangle inequality theorem and explain your reasoning.
Word Problem Maria has a piece of string that is 20 cm long. She wants to cut it into three pieces to form a triangle. What is the maximum length of the longest piece of string she can cut while still being able to form a triangle? Please explain your solution using the properties of triangle inequalities.