Question

can you find the missing side lengths?

Explanation:

Step1: Assume the triangles are similar

If \(\triangle ABC\) and \(\triangle DEC\) are similar, the ratios of corresponding - sides are equal. Let's assume \(\frac{AB}{DE}=\frac{AC}{DC}=\frac{BC}{EC}\).

Step2: Set up the proportion for known - sides

We know \(AB = 6\mathrm{cm}\), \(DE = 7.2\mathrm{cm}\), \(AC = 4\mathrm{cm}\), and \(DC = 10.8\mathrm{cm}\). Let's find the ratio of similarity. The ratio of \(AB\) to \(DE\) is \(\frac{AB}{DE}=\frac{6}{7.2}=\frac{60}{72}=\frac{5}{6}\).

Step3: Find side \(d\)

Using the proportion \(\frac{AC}{DC}=\frac{BC}{EC}\), we can also use the ratio of similarity to find \(d\). If we assume the ratio of corresponding sides of the two similar triangles is \(\frac{5}{6}\), and we know the relationship between the sides. Let's set up the proportion \(\frac{4}{10.8}=\frac{6}{d}\). Cross - multiply: \(4d=6\times10.8\). Then \(4d = 64.8\), and \(d=\frac{64.8}{4}=16.2\mathrm{cm}\).

Answer:

\(d = 16.2\mathrm{cm}\)