Question

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​

Answer 1

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