Question

g is the midpoint of \\(\overline{fh}\\). if \\(fg = 6x\\) and \\(fh = 11x + 3\\), what is \\(fh\\)?
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 \( \overline{FH} \), \( FG = GH \) and \( FH = 2 \times FG \). So we have the equation \( FH = 2 \times FG \), substituting the given expressions: \( 11x + 3 = 2(6x) \).

Step2: Solve for \( x \)

Simplify the right side: \( 11x + 3 = 12x \). Subtract \( 11x \) from both sides: \( 3 = 12x - 11x \), which gives \( x = 3 \).

Step3: Find \( FH \)

Substitute \( x = 3 \) into the expression for \( FH \): \( FH = 11(3) + 3 \). Calculate \( 11 \times 3 = 33 \), then \( 33 + 3 = 36 \).

Answer:

\( 36 \)