Question

10.
there is a triangle with a line segment parallel to the base (presumably, from the markings) dividing the sides proportionally. the base is labeled (5x + 26), the segment inside is labeled (4x + 1), and there are congruency markings on the sides (double and single ticks indicating equal segments).

Explanation:

Step1: Identify the midline theorem

The segment connecting the midpoints of two sides of a triangle (midline) is parallel to the third side and half its length. Here, the segment \(4x + 1\) is the midline, so it should be half of \(5x + 26\). So we set up the equation: \(2(4x + 1)=5x + 26\).

Step2: Solve the equation

Expand the left side: \(8x + 2 = 5x + 26\).
Subtract \(5x\) from both sides: \(8x - 5x+ 2 = 26\), which simplifies to \(3x + 2 = 26\).
Subtract 2 from both sides: \(3x = 26 - 2 = 24\).
Divide both sides by 3: \(x=\frac{24}{3}=8\).

Answer:

\(x = 8\)