which set if side lengths can form a traingle? A. 6, 8, an 16 centimeters B. 6, 8, and 10 centimeters C. 6, 7, and 14 centimeters D. 6,7, and 20 centimeters

Option b - 6, 8, and 10 centimeters can form a triangle

Step-by-step explanation:

Step 1:

Three lengths can be the sides of triangle if the 2 length's sum is always greater than length of third side. This should be true for all 3 combinations.

If p, q, r are 3 lengths then this will forma triangle if

p + q > r

q + r > p

p + r > q

Step 2:

a)

p = 6, q = 8, r = 16

p + q = 6 + 8 = 14

This is not greater than r = 16.

So these length cannot form a triangle.

Step 3:

b)

p = 6, q = 8, r = 10

p + q = 6 + 8 = 14. This is greater than r = 10

q + r = 8 + 10 = 18. This is greater than r = 6

p + r = 6 + 10 = 16. This is greater than r = 8

Since all the 3 inequalities are satisfied these lengths can form a triangle

Step 4:

c)

p = 6, q = 7, r = 14

p + q = 6 + 7 = 13

This is not greater than r = 14.

So these length cannot form a triangle.

Step 5:

d)

p = 6, q = 7, r = 20

p + q = 6 + 7 = 13

This is not greater than r = 20.

So these length cannot form a triangle.

Step 6:

Answer:

Option b is the correct answer