Question

find the value of x.
3x + 6
6
x = (simplify your answer.)

Explanation:

Step1: Apply the mid - segment theorem

The mid - segment of a triangle is parallel to the third side and half its length. Here, the mid - segment length is \(3x + 6\) and the third side length is \(2\times6=12\). So, \(3x + 6=\frac{1}{2}\times(3x + 6)\times2 = 12\).

Step2: Solve the equation for \(x\)

Subtract \(6\) from both sides of the equation \(3x+6 = 12\): \(3x=12 - 6\). Then \(3x = 6\). Divide both sides by \(3\): \(x=\frac{6}{3}=2\).

Answer:

\(x = 2\)