Question:
In the given figure, DE || BC in ∆ABC such that BC = 8 cm, AB = 6 cm and DA = 1.5 cm. Find DE.
Solution:
Given: In ∆ABC, DE || BC. BC = 8 cm, AB = 6 cm and DA = 1.5 cm.
To find: DE
In ∆ABC and ∆ADE
∠B=∠ADE Corresponding angles∠A=∠A Common∴∆ABC~∆ADE AA Similarity
So,
$\frac{\mathrm{BC}}{\mathrm{DE}}=\frac{\mathrm{AB}}{\mathrm{DA}}$
$\frac{8}{D E}=\frac{6}{1.5}$
$\mathrm{DE}=\frac{8 \times 1.5}{6}$
$\mathrm{DE}=2 \mathrm{~cm}$