Question

A triangle has two sides of length 9 and 6. What is the smallest possible whole-number length for the third side?

Answer 1

Answer:

c=4

Step-by-step explanation:

a=9, b=6, c=?

|a-b|<c<|a+b| (Triangle inequality)

|9-6|<c<|9+6|

|3|<c<|15|

3<c<15

then c=4 (smallest possible)

Answer 2

Answer:

4

Step-by-step explanation:

Let the third side = x.

The sum of any two sides must be greater than the third side

9+6 > x

15 > x

9 + x > 6

x > 6-9

x > -3

6+ x > 9

x > 9-6

x > 3

So 3 < x < 15

Therefore the smallest whole number length the third side could have is 4.

The largest whole number length the third side could  have is 14.

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