Question

A triangle has a side of length 8, a second side of length 17, and a third side of length x. Express the range of possible values for x as a compound inequality. The range of possible values for x is __

Answer 1

The most possible answer for x is 9 < x < 25

Answer 2

9 < x < 25

Explanation:

Given that:

• 1st side: 8
• 2nd side: 17
• 3rd side: x

As we know the third side cannot exceed the others added up (8+17)=15

so x is less than 25, due to the laws of triangles.

<=> x < 25 (1)

Moreover, the third side is greater than the difference of the other 2 sides

<=> x > 17-8

<=> x > 9 (2)

From (1) and (2), we have the range of possible values for x is:

9 < x < 25