Triangle Fundimentals

Question

Does each set of numbers represent the lengths of the sides of a triangle? 

a. 5, 8, 13   

b. 6, 17, 22 

c. 12, 12, 2  

d. 23, 9, 15

e. 4, 7, 12  

f. 22, 9, 14 

Answer 1

Hi, Emily! The rule for determining whether 3 lengths can make a triangle is this: the sum of the two shorter sides has to be greater than the longest side.

a. 5, 8, 13

Since 5 + 8 is not greater than 13 (the sum is 13), these three sides can't make a triangle.

b. 6, 17, 22

6 + 17 = 23. Since 23 is greater than 22, these three sides can make a triangle.

c. 12, 12, 2

If there are two numbers that are the same, the rule is that the third number needs to be smaller than the sum of the identical numbers. Since 2 is less than 12 + 12, these sides can make a triangle! (It wouldn't make a triangle if the third number was, for example, 25, because 25 is greater than 12 + 12.)

d. 23, 9, 15

9 + 15 = 24. Since 24 is greater than 23, these three sides can form a triangle.

e. 4, 7, 12

4 + 7 = 11. 11 is not greater than 12, so these sides cannot make a triangle.

f. 22, 9, 14

9 + 14 = 23. Since 23 is greater than 22, these three sides can make a triangle.

Hope this helps!