Question

in the figure below, de || bc
how long is bc?
7
8
10
18

Explanation:

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

Since \(DE\parallel BC\), we have \(\frac{AD}{DB}=\frac{AE}{EC}\). Let \(AD = 3\), \(DB=x\), \(AE = 6\), \(EC = 12\). But we can also use the ratio for the lengths of \(DE\) and \(BC\). The ratio of the segments of the sides gives the ratio of the parallel lines. The ratio of the segments of the side \(AC\) is \(\frac{AE}{AC}=\frac{6}{6 + 12}=\frac{6}{18}=\frac{1}{3}\).

Step2: Set up the proportion for \(DE\) and \(BC\)

We know that \(\frac{DE}{BC}=\frac{AE}{AC}\). Given \(DE = 4\), let \(BC=y\). Then \(\frac{4}{y}=\frac{6}{6 + 12}\). Cross - multiply: \(6y=4\times(6 + 12)\).

Step3: Solve the equation

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Answer:

\(12\)