Question

δabc ~ δdef
find the value of x.

x =

Explanation:

Step1: Use the property of similar triangles

For similar triangles \(\triangle ABC\) and \(\triangle DEF\), the ratios of corresponding sides are equal. So, \(\frac{AB}{DE}=\frac{BC}{EF}\).

Step2: Substitute the known values

We know \(AB = 2\) ft, \(BC=3\) ft, \(EF = 6\) ft, and \(DE=x\) ft. Substituting into the ratio \(\frac{AB}{DE}=\frac{BC}{EF}\), we get \(\frac{2}{x}=\frac{3}{6}\).

Step3: Solve the proportion for \(x\)

Cross - multiply: \(3x=2\times6\). Then \(3x = 12\). Divide both sides by 3: \(x=\frac{12}{3}\).

Answer:

\(x = 4\)