Question

Question 9
$In\Delta ABC\sim \Delta DFE,\angle A={30}^{\circ },\angle C={50}^{\circ },$ $AB=5cm,AC=8cmandDF=7.5cm$ ,then which of the following is true?

(A) $DE=12cm,\angle F={50}^{\circ }$
(B) $DE=12cm,\angle F={100}^{\circ }$
(C) $EF=12cm,\angle D={100}^{\circ }$
(D) $EF=12cm,\angle D={30}^{\circ }$

Answer 1

$Given:\Delta ABC\sim \Delta DFE,$
$\angle A=\angle D={30}^{\circ }and\angle C=\angle E={50}^{\circ }$



In $\Delta ABC$,
$\angle A+\angle B+\angle C={180}^{\circ }$
[Angle sum property of a triangle]
$\angle B={180}^{\circ }-\angle A-\angle C$
$\angle B={180}^{\circ }-{30}^{\circ }-{50}^{\circ }={100}^{\circ }$
$\therefore$ $\angle B=\angle F={100}^{\circ }$

$Also,AB=5cm,AC=8cm,andDF=7.5cm$
$\therefore \frac{AB}{DF}=\frac{AC}{DE}$
$\Rightarrow \frac{5}{7.5}=\frac{8}{DE}$
$\Rightarrow DE=\frac{8\times 7.5}{5}=12cm$

$\therefore DE=12cmand\angle F={100}^{\circ }$