Question

D and E are respectively the points on the sides AB and AC of ΔABC such that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE || BC. Then DE = ___________.

Answer 1

In ΔABC, D and E are points on the sides AB and AC, respectively such that DE || BC.



In ∆ADE and ∆ABC,

∠DAE = ∠BAC (Common)

∠AED = ∠ACB (Corresponding angles)

∴ ∆ADE $~$ ∆ABC (AA Similarity)

$\Rightarrow \frac{\mathrm{DE}}{\mathrm{BC}}=\frac{\mathrm{AD}}{\mathrm{AB}}$ (If two triangles are similar, then their corresponding sides are proportional)

$$\begin{gathered} \Rightarrow \frac{\mathrm{DE}}{7.5\mathrm{cm}}=\frac{2\mathrm{cm}}{5\mathrm{cm}}\left(\mathrm{AB}=\mathrm{AD}+\mathrm{BD}\right) \\ \Rightarrow \mathrm{DE}=\frac{7.5\times 2}{5}=3\mathrm{cm} \end{gathered}$$

D and E are respectively the points on the sides AB and AC of ΔABC such that AD = 2 cm, BD = 3 cm, BC = 7.5 cm and DE || BC. Then DE = _____3 cm______.