Question

given two similar triangles, as shown in the figure below, find the unknown length.
$b = 8$, $c = 15$, $c = 5$; find $b$.
$b =$
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Explanation:

Step1: Use the property of similar triangles

For similar triangles, the ratios of corresponding sides are equal. So, we have the proportion \(\frac{b}{b'}=\frac{c}{c'}\).

Step2: Substitute the given values into the proportion

Substitute \(b' = 8\), \(c'=15\), and \(c = 5\) into \(\frac{b}{b'}=\frac{c}{c'}\), we get \(\frac{b}{8}=\frac{5}{15}\).

Step3: Solve for \(b\)

Cross - multiply: \(15b=8\times5\). Then \(15b = 40\). Divide both sides by 15: \(b=\frac{40}{15}=\frac{8}{3}\approx2.67\).

Answer:

\(\frac{8}{3}\)