Question

3.11.2 preponderance of proportional relationships find the length of each unlabeled side. side length correct? ef ed \\(\overline{bd} \parallel \overline{fg}\\)

Explanation:

Step1: Use the basic proportionality theorem (Thales' theorem)

Since \( \overline{BD}\parallel\overline{FG}\), we have \(\frac{EB}{EF}=\frac{ED}{EG}=\frac{BD}{FG}\).
We know \(EB = 2.5\), \(BD = 5\), \(FG=15\), and \(EG=ED + 12\).
From \(\frac{EB}{EF}=\frac{BD}{FG}\), let \(EF=x\). Then \(\frac{2.5}{x}=\frac{5}{15}\).
Cross - multiply: \(5x=2.5\times15\).

Step2: Solve for \(EF\)

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Step3: Solve for \(ED\)

From \(\frac{ED}{ED + 12}=\frac{BD}{FG}\), let \(ED = y\). Then \(\frac{y}{y + 12}=\frac{5}{15}\).
Cross - multiply: \(15y=5(y + 12)\).
Expand: \(15y=5y+60\).
Subtract \(5y\) from both sides: \(15y-5y=60\), \(10y = 60\), \(y = 6\).

Answer:

Side	Length
\(ED\)	\(6\)