Question

1. if \\( \triangle abc \sim \triangle dec \\), find the value of \\( x \\) and \\( y \\).

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle ABC\sim\triangle DEC\), the ratios of corresponding sides are equal.
For side \(x\):
\(\frac{AB}{DE}=\frac{BC}{DC}\)
\(\frac{6}{21}=\frac{10}{x}\)
Cross - multiply: \(6x = 21\times10\)
\(6x=210\)
\(x=\frac{210}{6}=35\)

Step2: Use the property of similar triangles for side \(y\)

\(\frac{AC}{EC}=\frac{BC}{DC}\)
\(\frac{x}{y}=\frac{10}{28}\)
We know \(x = 35\), so \(\frac{35}{y}=\frac{10}{28}\)
Cross - multiply: \(10y=35\times28\)
\(10y = 980\)
\(y=\frac{980}{10}=98\)

Answer:

\(x = 35\), \(y = 98\)