Question

if ( ef = fg = 76 ), ( eh = c + 48 ), and ( gh = 7c ), what is the value of ( c )?

Explanation:

Step1: Apply the perpendicular bisector theorem

Since \(EF = FG = 76\), by the perpendicular bisector theorem, \(EH=GH\).

Step2: Set up the equation

We know that \(EH = c + 48\) and \(GH = 7c\). So, \(c + 48=7c\).

Step3: Solve the equation

Subtract \(c\) from both sides: \(48 = 7c - c\), which simplifies to \(48 = 6c\). Then divide both sides by \(6\): \(c=\frac{48}{6}\).

Answer:

\(8\)