Two sides of a triangle have lengths 7 and 18. Which inequalities represent the possible lengths for the third side, x?

Question

A. 11<x<25

B. 7<x<18

C. 11<x<18

D. 11<x<7

Answer 1

Hi Kayonna,

The triangle inequality theorem states that the sum of any two sides of a triangle is greater than the 3 side.

In this problem our triangle has three sides, 7, 18 and x, and we're asked to describe the range of all possible values for x.

Different teachers might have different approaches to this problem so I'm going to do it two ways.

One approach is to write all 3 inequalities that the inequality theorem states must be true.

7 + 18 > x

18 + x > 7

7 + x > 18

The first inequality can be reworked as 25 > x and then rewritten as x < 25

The second is really helpful. Since 18 is already greater than 7, only negative value of x would make this false and lengths CAN"T be negative.

If we solve the third inequality for x, by subtracting 7 we get x > 11.

x < 25 and x > 11 can be rewritten and combined as 11 < x < 25, which matches answer choice A.

Another approach, and one I actually prefer is even easier.

1. Take the two number that were given, 7 and 18.
2. Subtract them to get 18 - 7 = 11
3. Add them to get 7 + 18 = 25
4. x MUST be between the difference and the sum, 11 < x < 25.

I hope this helps.

Answer 2

A, 11<x<25

the third side cannot be greater than the sum of the other 2 sides x< 7+18=25, x<25

the third side cannot be less than the difference of the other 2 sides x> 18-7 = 11, x>11