Which three lengths cannot be the lengths of the sides of a triangle?
A)25 m, 16 m, 10 m
B)15 m, 13 m, 12 m
C)18 m, 5 m, 10 m
D)8 m, 8 m, 15 m
thanks so much!!! it worked. all are bigger than the third length except for c. :)
to form a triangle , the sum of any two lengths must be greater than the third length.
Look at C)
18+5> 10 ? , yes
18 + 10 > 5 ? , yes
5+10 > 18 ? , NO
the 3 sides cannot form a triangle
test the others the same way
Renvetjohn
To determine whether a set of three lengths can form a triangle, we need to check if it satisfies the triangle inequality theorem, which states that the sum of any two sides of a triangle must always be greater than the length of the third side.
Let's apply the theorem to each given set of lengths:
A) 25 m, 16 m, 10 m
- The sum of the two smaller sides (16 m and 10 m) is 26 m, which is greater than the largest side (25 m).
- The sum of the two remaining sides (25 m and 10 m) is 35 m, which is greater than the remaining side (16 m).
- The sum of the two remaining sides (25 m and 16 m) is 41 m, which is greater than the remaining side (10 m).
Therefore, the lengths 25 m, 16 m, and 10 m can form a triangle.
B) 15 m, 13 m, 12 m
- The sum of the two smaller sides (13 m and 12 m) is 25 m, which is greater than the largest side (15 m).
- The sum of the two remaining sides (15 m and 12 m) is 27 m, which is greater than the remaining side (13 m).
- The sum of the two remaining sides (15 m and 13 m) is 28 m, which is greater than the remaining side (12 m).
Therefore, the lengths 15 m, 13 m, and 12 m can form a triangle.
C) 18 m, 5 m, 10 m
- The sum of the two smaller sides (5 m and 10 m) is 15 m, which is not greater than the largest side (18 m).
Therefore, the lengths 18 m, 5 m, and 10 m cannot form a triangle.
D) 8 m, 8 m, 15 m
- The sum of the two smaller sides (8 m and 8 m) is 16 m, which is not greater than the largest side (15 m).
Therefore, the lengths 8 m, 8 m, and 15 m cannot form a triangle.
Therefore, the correct answer is C) 18 m, 5 m, and 10 m.