Question

If it is given that ∆ABC ~ ∆EDF such that AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm. Then, BC = ______ and EF = _______.

Answer 1

∆ABC ~ ∆EDF (Given)

$\therefore \frac{\mathrm{AB}}{\mathrm{ED}}=\frac{\mathrm{BC}}{\mathrm{DF}}=\frac{\mathrm{AC}}{\mathrm{EF}}$ (If two triangles are similar, then their corresponding sides are proportional)

$$\begin{gathered} \Rightarrow \frac{5\mathrm{cm}}{12\mathrm{cm}}=\frac{\mathrm{BC}}{15\mathrm{cm}}=\frac{7\mathrm{cm}}{\mathrm{EF}} \\ \Rightarrow \frac{5}{12}=\frac{\mathrm{BC}}{15\mathrm{cm}}\mathrm{and}\frac{5}{12}=\frac{7\mathrm{cm}}{\mathrm{EF}} \\ \Rightarrow \mathrm{BC}=\frac{5\times 15}{12}=\frac{25}{4}\mathrm{cm}\mathrm{and}\mathrm{EF}=\frac{7\times 12}{5}=\frac{84}{5}\mathrm{cm} \end{gathered}$$

⇒ BC = 6.25 cm and EF = 16.8 cm

If it is given that ∆ABC ~ ∆EDF such that AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm. Then, BC = __6.25 cm__ and EF = __16.8 cm__.