Which of the following side lengths could combine to form a triangle?
a. 17, 13, 2
b. 15, 18, 24
c. 5, 9, 14
d. 16, 32, 16
To form a triangle, the sum of any two sides must be greater than the remaining third side
checking for a)
is 17+13> 2 ? Yes
is 17+2 > 13 ? Yes
is 13+2 > 17 ? NO
So 17,13,2 cannot form a triangle
Repeat for the others.
thank you
To determine if a set of side lengths can form a triangle, we use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
Let's check each set of side lengths:
a. 17, 13, 2
To form a triangle, the sum of any two sides must be greater than the third side:
17 + 13 = 30 and 30 > 2
The side lengths 17, 13, 2 can form a triangle.
b. 15, 18, 24
15 + 18 = 33 and 33 > 24
18 + 24 = 42 and 42 > 15
15 + 24 = 39 and 39 > 18
The side lengths 15, 18, 24 can form a triangle.
c. 5, 9, 14
5 + 9 = 14 and 14 > 14
9 + 14 = 23 and 23 > 5
5 + 14 = 19 and 19 > 9
The side lengths 5, 9, 14 can form a triangle.
d. 16, 32, 16
16 + 32 = 48 and 48 > 16
32 + 16 = 48 and 48 > 16
16 + 16 = 32 and 32 > 16
The side lengths 16, 32, 16 can form a triangle.
Therefore, the correct answer is:
a. 17, 13, 2
b. 15, 18, 24
c. 5, 9, 14
d. 16, 32, 16