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 units b) 6x units c) 5x + 2 units d) 9x – 6 units

Option B: 6x units is the answer.

Step-by-step explanation:

Two sides of a triangle measure 2x – 4 and 7x – 2 units.

According to the Triangle Inequality Theorem we know that the sum of any two sides of a triangle must be greater than the measure of the third side.

Let the third side be = y

This gives:

Solving this we get,

We also know that the difference of two sides of a triangle is less than third side.

=

Now the range for the 3rd side or 'y' lies between:

Now option A: 3x does not lie in the interval.

Option B : 6x is in the interval.

Option C and option D are the ranges. They do not lie within the interval.

Therefore, option B is the answer.

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