Question

if fg = 18, gh = 2x, and fh = 5x + 3, 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 expressions: $5x + 3=18+2x$.

Step2: Solve for x

Subtract $2x$ from both sides: $5x-2x + 3=18+2x-2x$, which simplifies to $3x + 3=18$. Then subtract 3 from both sides: $3x+3 - 3=18 - 3$, giving $3x=15$. Divide both sides by 3: $x = 5$.

Step3: Find the value of GH

Since $GH = 2x$ and $x = 5$, then $GH=2\times5=10$.

Answer:

10