Question

Determine whether the three segment lengths will produce a triangle. Type yes or no in the space provided.

Answer 1

Answer:

20 , 20 , 30 will produce a triangle

Step-by-step explanation:

* Lets study how to know if the lengths of the three segments

 can formed a triangle

- It is a fact that in any triangle the sum of the smallest two sides

 must be greater than the largest side

- Lets study some examples

# If the lengths of the three segments are 5 , 6 , 7

∵ 5 and 6 are the smallest

∴ 5 + 6 = 11

∵ 11 > 7 ⇒ the sum greater than the 3rd side

∴ 5 , 6 , 7 can formed a triangle

# If the lengths of the three segments are 5 , 7 , 12

∵ 5 and 7 are the smallest

∴ 5 + 7 = 12

∵ 12 = 12 ⇒ the sum equal the 3rd side

∴ 5 , 7 , 12 can not formed a triangle

# If the lengths of the three segments are 10 , 12 , 24

∵ 10 and 12 are the smallest

∴ 10 + 12 = 22

∵ 22 < 24 ⇒ the sum less than the 3rd side

∴ 10 , 12 , 24 can not formed a triangle

* Now lets solve the problem

∵ The length of the three segments are 20 , 20 , 30

∵ 20 and 20 are the smallest

∴ 20 + 20 = 40

∵ 40 > 30 ⇒ the sum greater than the 3rd side

∴ 20 , 20 , 30 will produce a triangle