Question

△abc is similar to △dec. find the length of x.
the length of side x is □□m.

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle ABC\sim\triangle DEC\), the ratios of their corresponding sides are equal. That is \(\frac{BC}{EC}=\frac{AB}{DE}\)

Step2: Substitute the known values

We know that \(BC = x\), \(EC=3.4 + 2.6=6\)m, \(AB = 7.8\)m, \(DE = 2.6\)m. Substituting into \(\frac{BC}{EC}=\frac{AB}{DE}\), we get \(\frac{x}{6}=\frac{7.8}{2.6}\)

Step3: Solve for \(x\)

Cross - multiply: \(2.6x=7.8\times6\). Then \(2.6x = 46.8\). Divide both sides by \(2.6\): \(x=\frac{46.8}{2.6}=18\)

Answer:

\(18\)