Question

△cde ~ △cts

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle CDE\sim\triangle CTS\), the ratios of corresponding sides are equal. Let the unknown side in \(\triangle CDE\) be \(x\). Then \(\frac{x}{20}=\frac{60}{17}\) (This is incorrect, actually for similar triangles \(\triangle CDE\sim\triangle CTS\), the ratio of corresponding sides: if we assume the side \(CD\) in \(\triangle CDE\) corresponds to \(TS\) in \(\triangle CTS\) and \(ED\) corresponds to \(CS\) (but wait, no, correct ratio is \(\frac{CD}{CT}=\frac{ED}{CS}\), no, wait the ratio of sides of similar triangles \(\triangle CDE\sim\triangle CTS\) gives \(\frac{CD}{CT}=\frac{DE}{TS}\). Let the unknown side \(CD = x\), \(CT = 17\), \(DE=60\), \(TS = 20\). So \(\frac{x}{17}=\frac{60}{20}\))

Step2: Solve the proportion

Cross - multiply the proportion \(\frac{x}{17}=\frac{60}{20}\). We get \(20x=17\times60\). Then \(x=\frac{17\times60}{20}\). Calculate \(17\times3 = 51\) (because \(\frac{60}{20}=3\))

Answer:

\(51\)