Question

5.
find x. give only the number.
answer

Explanation:

Step1: Use the triangle mid - segment theorem

The triangle mid - segment theorem states that the length of the mid - segment is half the length of the third side. Here, the segment with length \(2x - 12\) is a mid - segment. The length of the third side is \(2 + 1+3=6\). According to the theorem, \(2x-12=\frac{1}{2}\times(2 + 1+3)\).

Step2: Solve the equation for \(x\)

First, simplify the right - hand side of the equation: \(\frac{1}{2}\times6 = 3\). So the equation becomes \(2x-12 = 3\). Add \(12\) to both sides: \(2x=3 + 12\), \(2x=15\). Then divide both sides by \(2\): \(x=\frac{15}{2}=7.5\).

Answer:

\(7.5\)