Question

find the value of x.
x = \square

Explanation:

Step1: Use the mid - segment theorem

The mid - segment of a triangle is parallel to the third side and half its length. Here, the segment of length \(3x\) is a mid - segment. The length of the non - parallel side of the larger triangle is \(30\).

Step2: Set up the equation

According to the mid - segment theorem, \(3x=\frac{30}{2}\).

Step3: Solve the equation

Simplify the right - hand side: \(\frac{30}{2} = 15\). Then, for \(3x=15\), divide both sides by \(3\): \(x=\frac{15}{3}\).

Answer:

\(5\)