Question

if (fg = 4x), (gh=x + 6), and (fh = 16), 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: $16 = 4x+(x + 6)$.

Step2: Combine like - terms

Combine the $x$ terms on the right - hand side: $16=4x+x + 6$, which simplifies to $16 = 5x+6$.

Step3: Isolate the variable term

Subtract 6 from both sides of the equation: $16−6=5x+6 - 6$, resulting in $10 = 5x$.

Step4: Solve for $x$

Divide both sides by 5: $\frac{10}{5}=\frac{5x}{5}$, so $x = 2$.

Step5: Find the value of $GH$

Substitute $x = 2$ into the expression for $GH$. Since $GH=x + 6$, then $GH=2 + 6=8$.

Answer:

8