Question

fg = 8x + 4. if gh = 4x + 8 and fh = 15x - 9, then fg = ?

Explanation:

Step1: Use segment - addition postulate

Since $FH = FG+GH$, we substitute the given expressions: $15x - 9=(8x + 4)+(4x + 8)$.

Step2: Simplify the right - hand side

Combine like terms on the right - hand side: $(8x + 4)+(4x + 8)=8x+4x + 4 + 8=12x+12$. So, $15x - 9=12x+12$.

Step3: Solve for x

Subtract $12x$ from both sides: $15x-12x - 9=12x-12x + 12$, which gives $3x-9 = 12$. Then add 9 to both sides: $3x-9 + 9=12 + 9$, so $3x=21$. Divide both sides by 3: $x = 7$.

Step4: Find the length of FG

Substitute $x = 7$ into the expression for $FG$. Since $FG=8x + 4$, then $FG=8\times7+4=56 + 4=60$.

Answer:

60