Answer:
7. yes, obtuse
8. no triangle
Step-by-step explanation:
7.
3, 7, 9
Do these side lengths form a triangle?
Add the two smaller numbers: 3 + 7 = 10
Since 10 is greater than 9, these three side lengths do form a triangle.
Now we qualify the triangle.
c^2 ? a^2 + b^2
The ? is there because we don';t know yet if it will be =, >, or <.
9^2 ? 3^2 + 7^2
81 ? 9 + 49
81 ? 58
Since 81 is greater than 58, now we know to use >.
81 > 58
Since c^2 is greater than a^ + b^2, the triangle is obtuse.
Answer: Yes these side lengths form a triangle, and the triangle is obtuse.
8.
4, 11, 16
Add the two small lengths: 4 + 11 = 15
Since 15 < 16, these three side lengths do not form a triangle.
Answer: no triangle
