Answer:
A) 13, 10, 16
Step-by-step explanation:
The Triangle Inequality Theorem will help you solve this question. The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
The options that are given are:
- A) 13, 10, 16
- B) 1, 2, 3
- C) 5.2, 11, 4.9
- D) 208, 9, 219
Lets solve each one to figure out if they could be the lengths of a triangle.
A) 13, 10, 16.
We can write three inequalities to see if the lengths are true.
13 + 10 > 16
10 + 16 > 13
13+ 16 > 10
Solve each one.
23 > 16
26 > 13
29 > 10
According to the information above, the set of numbers from option A does fit the Triangle Inequality Theorem. Therefore, they are possible lengths.
B) 1, 2, 3
Write three inequalities:
1 + 2 > 3
2 + 3 > 1
3+ 1 > 2
Solve each.
3 > 3
5 > 1
4 > 2
As you see, only two lengths fit the theorem, but the third side (3 > 3) does not. This set of lengths is not a possible set for a triangle.
C) 5.2, 11, 4.9
Write three inequalities:
5.2 + 11 > 4.9
4.9 + 11 > 5.2
5.2 + 4.9 > 11
Solve each.
16.2 > 4.9
15.9 > 5.2
10.1 > 11
As you see, only two sides lengths can repsent the lengths of a triangle but the third does not, so its not a possible set of lengths for a triangle.
D) 208, 9, 219
Write three inequalities:
208 + 9 > 219
219 + 9 > 208
208+ 219 > 9
Solve each.
217 > 219
228 > 208
427 > 9
Although two lengths fit the theorem, one length does not, so this a not a possible set of lengths.
In summary, only one set of lengths is possible for a triangle, with is A.
