Question

find the length of ab

Explanation:

Step1: Use the mid - segment theorem

The mid - segment theorem states that the length of the mid - segment of a triangle (a segment connecting the mid - points of two sides of a triangle) is half the length of the third side. Here, \(AB\) is the mid - segment of \(\triangle XYZ\) (assuming \(A\) and \(B\) are mid - points). So, \(AB=\frac{1}{2}\times XZ\).

Step2: Set up the equation

We know that \(AB = 3x - 1\) and \(XZ=34\). By the mid - segment theorem \(3x - 1=\frac{1}{2}\times34\).
First, simplify the right - hand side: \(\frac{1}{2}\times34 = 17\). Then the equation becomes \(3x-1 = 17\).
Add \(1\) to both sides: \(3x=17 + 1=18\).
Divide both sides by \(3\): \(x = 6\).

Step3: Calculate the length of \(AB\)

Substitute \(x = 6\) into \(AB=3x - 1\). Then \(AB=3\times6-1=18 - 1=17\).

Answer:

\(17\)