Question

1. if \\( \triangle a b c \sim \triangle a v w \\), find the values of \\( x \\) and \\( y \\).

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle ABC\sim\triangle A VW\), the ratios of corresponding sides are equal. That is \(\frac{BC}{VW}=\frac{AB}{AV}=\frac{AC}{AW}\).

Step2: Find the value of \(x\)

We know \(BC = 16\), \(VW=10\), \(AC = 28\), \(AW=x + 12\). Using \(\frac{BC}{VW}=\frac{AC}{AW}\), we have \(\frac{16}{10}=\frac{28}{x + 12}\). Cross - multiply: \(16(x + 12)=28\times10\). Expand: \(16x+192 = 280\). Subtract 192 from both sides: \(16x=280 - 192=88\). Divide by 16: \(x=\frac{88}{16}=\frac{11}{2}=5.5\).

Step3: Find the value of \(y\)

Using \(\frac{BC}{VW}=\frac{AB}{AV}\), let \(AB = y\), \(AV = 12\). So \(\frac{16}{10}=\frac{y}{12}\). Cross - multiply: \(10y=16\times12\). Then \(y=\frac{16\times12}{10}=\frac{192}{10}=19.2\).

Answer:

\(x = 5.5\), \(y = 19.2\)