Question

given two similar triangles, as shown in the figure below, find the unknown length.
( b = 5 ), ( c = 15 ), ( b = 3 ); find ( c ).
( c = )

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 \(b = 5\), \(c = 15\), and \(b'=3\) into \(\frac{b}{b'}=\frac{c}{c'}\), we get \(\frac{5}{3}=\frac{15}{c'}\).

Step3: Solve for \(c'\)

Cross - multiply: \(5\times c'=3\times15\), which simplifies to \(5c' = 45\). Then divide both sides by 5: \(c'=\frac{45}{5}\).

Answer:

\(9\)