Question

given two similar triangles, as shown in the figure below, find the unknown length.
( b = 5 ), ( c = 20 ), ( b ^ { prime } = 3 ); find ( c ^ { prime } ).
( c ^ { prime } = )

Explanation:

Step1: Use the property of similar triangles

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

Step2: Substitute the given values

Given \(b = 5\), \(c = 20\), \(b'=3\). Substitute into \(\frac{b}{b'}=\frac{c}{c'}\), we get \(\frac{5}{3}=\frac{20}{c'}\).

Step3: Solve for \(c'\)

Cross - multiply: \(5\times c'=3\times20\), so \(5c' = 60\). Then \(c'=\frac{60}{5}\).

Answer:

\(12\)