Question

g is the midpoint of \\(\overline{fh}\\). if \\(fg = 8x\\) and \\(gh = 4x + 5\\), what is \\(fg\\)? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use midpoint property

Since \( G \) is the midpoint of \( \overline{FH} \), \( FG = GH \). So we set up the equation \( 8x = 4x + 5 \).

Step2: Solve for \( x \)

Subtract \( 4x \) from both sides: \( 8x - 4x = 4x + 5 - 4x \), which simplifies to \( 4x = 5 \). Then divide both sides by 4: \( x=\frac{5}{4} \).

Step3: Find \( FG \)

We know \( FG = 8x \), substitute \( x = \frac{5}{4} \) into it: \( FG = 8\times\frac{5}{4} \). Calculate \( 8\times\frac{5}{4}=10 \).

Answer:

\( 10 \)