Question

fill in the blank 1 point
find gh.
d
9x - 59
x = 11.3
gh = 23.3

Explanation:

Step1: Use the mid - segment theorem

In a triangle, the mid - segment is parallel to the third side and half its length. Here, \(GH\) is the mid - segment of \(\triangle DEF\), so \(3x - 4=\frac{1}{2}(9x - 59)\).

Step2: Solve the equation for \(x\)

Multiply both sides of the equation \(3x - 4=\frac{1}{2}(9x - 59)\) by \(2\) to get \(6x-8 = 9x - 59\).
Then, move the \(x\) terms to one side: \(6x-9x=-59 + 8\).
Simplify: \(-3x=-51\), so \(x = 17\).

Step3: Find the length of \(GH\)

Substitute \(x = 17\) into the expression for \(GH\). Since \(GH=3x - 4\), then \(GH=3\times17-4\).
Calculate: \(GH = 51-4=47\).

Answer:

\(47\)