Which of the following could be the lengths of the sides of a triangle?
A. 1, 3, and 4 units
B. 2, 3, and 6 units
C. 4, 4.5, and 5 units
D. 3.5, 4.5, and 8 units
This is on my STAAR packet for extra credit so please help ASAP!!!!!
Not A, you can make a straight line
Not B, 2+3 is shorter than 6
no problem with 4, 4.5 and 5
D is exactly the same problem as A, straight line
So, it's C, right?
Well, of course it is up to you. That just happens to be my pick.
Get a compass and ruler and try to draw them all :)
Ok, thanks for your help!
To determine which of the given options could be the lengths of the sides of a triangle, we need to apply 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 go through each option and see if it satisfies the triangle inequality theorem:
A. 1, 3, and 4 units:
The sum of the two shorter sides (1 + 3 = 4) is equal to the length of the longest side (4). This means it could form a degenerate triangle, where the three sides lie on the same line.
B. 2, 3, and 6 units:
The sum of the two shorter sides (2 + 3 = 5) is less than the length of the longest side (6). So, this option does not satisfy the triangle inequality theorem.
C. 4, 4.5, and 5 units:
The sum of the two shorter sides (4 + 4.5 = 8.5) is greater than the length of the longest side (5). This option satisfies the triangle inequality theorem.
D. 3.5, 4.5, and 8 units:
The sum of the two shorter sides (3.5 + 4.5 = 8) is equal to the length of the longest side (8). This could form a degenerate triangle as well.
Based on the triangle inequality theorem, option C (4, 4.5, and 5 units) is the only set of lengths that could form a valid triangle. Therefore, the correct answer is C.