Question

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. The lengths of two sides of a triangle are 17 ft and 22 ft. Find the possible lengths of the third side.

Answer 1

Answer:

Any c answer that fits 5 <c<37 is correct.

Step-by-step explanation:

Say the three sides of the triangle are  

a

,

b

and  

c

. Here,  

a

=

16

and  

b

=

21

. We must find the possible values of  

c

.

Since  

a

+

c

>

b

, we can input:

16

+

c

>

21

c

>

5

.

So the lower bound of  

c

is everything above  

5

.

We also know that  

a

+

b

>

c

. Inputting:

16

+

21

>

c

37

>

c

.

So  

c

must be less than, but not including  

37

.

In conclusion, the side length  

c

must satisfy the following inequality:

Answer 2

Answer:

The answer C

Step-by-step explanation: