Question

if fg = 20, gh = x + 20, and fh = 6x + 10, 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: $6x + 10=20+(x + 20)$.

Step2: Simplify the right - hand side

$6x + 10=x + 40$.

Step3: Subtract $x$ from both sides

$6x - x+10=x - x + 40$, which gives $5x+10 = 40$.

Step4: Subtract 10 from both sides

$5x+10 - 10=40 - 10$, so $5x=30$.

Step5: Solve for $x$

Divide both sides by 5: $\frac{5x}{5}=\frac{30}{5}$, then $x = 6$.

Step6: Find the value of $GH$

Substitute $x = 6$ into the expression for $GH$. Since $GH=x + 20$, then $GH=6 + 20$.
$GH=26$.

Answer:

$26$