Question

the diagram is not drawn to scale. 20. 2x - 8. 23. find the value of x. 14 10 9 11

Explanation:

Step1: Identify mid - segment theorem

In a triangle, if a line segment joins the mid - points of two sides of a triangle, then the line segment is parallel to the third side and its length is half of the length of the third side. Here, the segment of length \(2x - 8\) is half of the side of length 20.

Step2: Set up the equation

We can set up the equation \(2x-8=\frac{20}{2}\).

Step3: Simplify the right - hand side

\(\frac{20}{2}=10\), so the equation becomes \(2x - 8=10\).

Step4: Solve for x

Add 8 to both sides of the equation: \(2x=10 + 8\), so \(2x=18\). Then divide both sides by 2: \(x=\frac{18}{2}=9\).

Answer:

9