Question

if \\( \triangle abc \sim \triangle def \\), find the value of \\( x \\).

6
15
9
11

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle ABC\sim\triangle DEF\), the ratios of corresponding sides are equal. That is \(\frac{AB}{DE}=\frac{AC}{DF}=\frac{BC}{EF}\). Here, we use \(\frac{AB}{DE}=\frac{BC}{EF}\). \(AB = 15\), \(BC=18\), \(EF = 12\), \(DE=x + 1\).

Step2: Set up the proportion

\(\frac{15}{x + 1}=\frac{18}{12}\). Cross - multiply: \(18(x + 1)=15\times12\).

Step3: Expand and solve the equation

Expand \(18(x + 1)\) to get \(18x+18\). So, \(18x+18 = 180\). Subtract 18 from both sides: \(18x=180 - 18=162\). Divide both sides by 18: \(x=\frac{162}{18}=9\).

Answer:

\(9\)