Question:
If ΔABC ~ΔDFE, ∠A = 30°, ∠C = 50°, AB = 5 cm, AC = 8 cm and OF = 7.5 cm. Then, which of the following is true?
(a) DE =12 cm, ∠F =50°
(b) DE = 12 cm, ∠F =100°
(c) EF = 12 cm, ∠D = 100°
(d) EF = 12 cm,∠D =30°
Solution:
(b) Given, AABC ~ ADFE, then ∠A = ∠D = 30°, ∠C = ∠E = 50°
$\therefore \quad \angle B=\angle F=180^{\circ}-\left(30^{\circ}+50^{\circ}\right)=100^{\circ}$
Also, $\quad A B=5 \mathrm{~cm}, A C=8 \mathrm{~cm}$ and $D F=7.5 \mathrm{~cm}$
$\therefore$ $\frac{A B}{D F}=\frac{A C}{D E}$
$\Rightarrow$ $\frac{5}{7.5}=\frac{8}{D E}$
$\therefore$ $D E=\frac{8 \times 7.5}{5}=12 \mathrm{~cm}$
Hence, $D E=12 \mathrm{~cm}, \angle F=100^{\circ}$