Question

If two sides of a triangle are 6 and 16, what is the range of the possible lengths of the third side?

Answer 1

10 < c < 22

Explanation:

Remember the Triangle Inequality Theorem.

For a triangle with sides a, b, and c:

- a + b > c

- a + c > b

- b + c > a

Let's arbitrarily say a = 6 and b = 16. Then:

a + b > c

6 + 16 > c

c < 22

a + c > b

6 + c > 16

c > 10

b + c > a

16 + c > 6

c > -10

Thus, the range of possible lengths of the third side, c, is 10 < c < 22.

Answer 2

10 < x <22

Explanation:

The smallest side must be larger than the difference of the two sides

16-6 = 10

x>10

The largest side must be smaller then the sum of the two sides

6+16 =22

x< 22

Put this together

10 < x <22