Question

if fg = 6x - 18, gh = 13x, and fh = 18x, what is fh? 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: $18x=(6x - 18)+13x$.

Step2: Combine like - terms

$18x=6x+13x - 18$, which simplifies to $18x = 19x-18$.

Step3: Solve for $x$

Subtract $18x$ from both sides: $0=19x - 18x-18$, so $x = 18$.

Step4: Find $FH$

Substitute $x = 18$ into the expression for $FH$. Since $FH = 18x$, then $FH=18\times18=324$.

Answer:

324