Question

if (fg = 3), (gh=x + 1), and (fh = 3x), what is (gh?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use segment - addition postulate

Since $FH=FG + GH$, we substitute the given values: $3x=3+(x + 1)$.

Step2: Simplify the right - hand side

$3x=3+x + 1$, which simplifies to $3x=x + 4$.

Step3: Solve for x

Subtract x from both sides: $3x−x=x + 4−x$, so $2x=4$. Then divide both sides by 2: $x = 2$.

Step4: Find the value of GH

Since $GH=x + 1$, substitute $x = 2$ into the expression for $GH$. So $GH=2 + 1=3$.

Answer:

3