Question

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

Answer 1

A because you all the values together with the value of a and set it equal to 180. Then whatever you get for “x” you find the values of each angle and see if they all add to 180 degrees.

Answer 2

Option B: 6x units is the answer.

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:
`2x-4+7x-2>y`

Solving this we get,

`9x-6>y`

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

`7x-2-(2x-4)` =
`5x+2`

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

`5x+2<y<9x-6`

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.