SORRY I FORGOT SOME QUESTI IN MY LAST POST!!!

The lengths of two sides of a triangle are given. Describe the possible lenths for the third side.

19.) 5,11
20.) 12,12
21.) 25,10
22.) 6,8

25.) A student draws a triangle with a perimeter 36 cm. The students says that the longest side measures 18 cm. How do you know that the student is incorrect? Explain.

No problem! I'll explain the possible lengths for the third side in each of the given cases and why the student's statement is incorrect.

19.) To find the possible lengths for the third side, you can use 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.

For the lengths 5 cm and 11 cm, the possible range of the third side would be:
11 - 5 < third side < 11 + 5
6 < third side < 16

So, the possible lengths for the third side range from 6 cm to 16 cm.

20.) In this case, both sides have the same length of 12 cm. Since the sum of any two sides must be greater than the length of the third side, for two sides with equal lengths, the third side must also have the same length.

Therefore, the possible length for the third side is 12 cm.

21.) Similar to the first case, we need to apply the Triangle Inequality Theorem. The range of the possible length of the third side is:
25 - 10 < third side < 25 + 10
15 < third side < 35

So, the possible lengths for the third side range from 15 cm to 35 cm.

22.) Applying the Triangle Inequality Theorem again, we get:
8 - 6 < third side < 8 + 6
2 < third side < 14

Therefore, the possible lengths for the third side range from 2 cm to 14 cm.

25.) The student claims that the longest side measures 18 cm. However, according to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, if the longest side is 18 cm, the other two sides must have a combined length greater than 18 cm. But the student also states that the perimeter of the triangle is 36 cm.

Therefore, the longest side cannot possibly be 18 cm, as the other two sides would have to be 18 cm each, resulting in a perimeter of 36 cm. This contradicts the information provided.

Hence, we can conclude that the student's statement is incorrect.