Two sides of a triangle measure 2x - 4 and 7x - 2 units, respectively. Which of these is a possible length for the third side of the triangle?

A 3X

B 6X

C 5X+2

D 9X-6

The lengths of the sides of a triangle must all be a positive number of units. For this reason, since 2x - 4 and 7x - 2 must both be positive, x must be greater than 2, and when x is greater than 2, 7x - 2 is always greater than 2x - 4. Thus, the third side of the triangle must be less than (7x - 2) + (2x - 4) units long and greater than (7x - 2) - (2x - 4) units long. In other words, it must be less than 9x - 6 units long and greater than 5x + 2 units long. Therefore, a possible length for the third side of the triangle is 6x units.

B. 6x.

Step-by-step explanation:

Given two sides of a triangle 2x - 4 and 7x - 2 units.

Difference of two sides of a triangle is less than third side.

Let us find the difference of 7x - 2 and 2x - 4, we get

7x-2 - (2x-4) = 7x - 2 - 2x + 4

= 5x + 2.

Third side should be less then 5x+2, so 5x+2 can't be third side.

Sum of two sides is greater than third side.

Adding given sides of triangle, we get

7x-2 + 2x-4 = 9x - 6.

Third side should be greater than 9x-6. So, 9x-6 can't be third side.

Now, if we add 3x and 2x-4, we get

3x+2x-4 = 5x-4, which is less than 9x - 6.

So, 3x can't be third side.

Therefore, correct option is:

B. 6x