Question

3.11.2 preponderance of proportional relationships
find the length of each unlabeled side.

(image of a triangle with segments: fg = 15, bd = 5, eb = 7.5, and bd || fg. table with sides ef (length 7.5, marked correct) and ed (length 6, marked incorrect, try again).)

Explanation:

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

Since \(BD\parallel FG\), we have the proportion \(\frac{EB}{BF}=\frac{ED}{DG}\). Given \(EB = 5\), \(BF=15\), \(DG = 12\). Substitute into the proportion \(\frac{5}{15}=\frac{ED}{12}\).

Step2: Solve the proportion for \(ED\)

Cross - multiply: \(15\times ED=5\times12\). Then \(15ED = 60\). Divide both sides by 15: \(ED=\frac{60}{15}=4\).

Answer:

\(ED = 4\)