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
