Question

4 fill in the blank 1 point find gh. navigate to question at position 4, unanswered x = type your answer... gh = type your answer...

Explanation:

Step1: Use the mid - segment theorem

In a triangle, the mid - segment (a segment connecting the mid - points of two sides of a triangle) is parallel to the third side and half its length. Here, \(GH\) is the mid - segment of \(\triangle DEF\). So, \(2(2x)=9x - 59\).

Step2: Solve the equation for \(x\)

Expand the left - hand side: \(4x=9x - 59\).
Subtract \(4x\) from both sides: \(0 = 9x-4x - 59\), which simplifies to \(0 = 5x-59\).
Add \(59\) to both sides: \(5x=59\), then \(x=\frac{59}{5}=11.8\).

Step3: Find the length of \(GH\)

Since \(GH = 2x\), substitute \(x = 11.8\) into the formula. So, \(GH=2\times11.8 = 23.6\).

Answer:

\(x = 11.8\), \(GH=23.6\)