Geometry math question

Question

Two sides of a triangle have lengths 5 and 4. Which of the following can NOT be the length of the third side.

A)4

B)3

C)1

D)2

 

Answer 1

If the 3 sides of a triangle are a, b, and c, the triangle in equality theorem says we must have:

• a+b>c
• a+c>b
• b+c>a

 

The problem gives you a = 5, b = 4.  Try each of the given options (A thru D) as c and test them against the three inequalities above.  If all of the inequalities are true, then the three sides can make a triangle.  If one or more of the inequalities are false, you cannot make a triangle.

 

I'll do A).  Set c = 4 (a=5, b=4):

• a+b>c, 5+4>4, 9>4 true
• a+c>b, 5+4>4, 9>4 true
• b+c>a, 4+4>5, 8>5 true

 

Yup these three lengths can make a triangle.  You test B), C), and D).

 

Answer 2

The sum of two sides of a triangle must be more than the third side.

 

When given two sides of a triangle, you can find a range of possible values for the third by doing this:

 

Find the difference in the two numbers (5-4 = 1)

 

Find the sum of the two numbers (5+4 =9)

 

The third side must be more than the lower number, which is 1 in this case, and must be less than 9.

 

1 < third side < 9

 

The answer is (C) because the third side must be greater than 1