Question

1. 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 \(FG\)

Substitute \(x = 7\) into the expression for \(FG\): \(FG=8x + 4\). Then \(FG=8\times7+4=56 + 4=60\).

Answer:

60