It is given that ABC DEF. If A =30^ , C =50^ , AB =5 cm, AC =8 cm… - Vidyadip

MCQ

It is given that $\triangle ABC \sim \triangle DEF$. If $\angle A =30^{\circ}$, $\angle C =50^{\circ}, AB =5 cm, AC =8 cm$ and $DF =7.5 cm$ then which of the following is true?

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

✓

Answer

Correct option: B.

$DE =12 cm, \angle F =100^{\circ}$

(b)
$
\angle B=180^{\circ}-\left(30^{\circ}+50^{\circ}\right)=180^{\circ}-80^{\circ}=100^{\circ}
$
Since $\triangle ABC \sim \triangle DFE$,
We have $\angle D =\angle A =30^{\circ}, \angle F =\angle B =100^{\circ}$ and $\angle E$ $=\angle C =50^{\circ}$.
Let $DE = x cm$. Then,
$
\frac{AB}{DF}=\frac{AC}{DE} \Rightarrow \frac{5}{7.5}=\frac{8}{x}
$
$
\Rightarrow 5 x=8 \times 7.5 \Rightarrow x=\frac{8 \times 7.5}{5}=12
$
Hence, $DE =12 cm$ and $\angle F =100^{\circ}$

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