MCQ
Choose the correct answer from the given four options:
It is given that $\triangle\text{ABC}\sim\triangle\text{DEF},\ \angle\text{A}=30^\circ,\ \angle\text{C}=50^\circ,$ AB = 5cm, AC = 8cm, and DF = 7.5cm Then, the following is true:
  • A
    $\text{DE}=12\text{cm},\angle\text{F}=50^\circ$
  • $\text{DE}=12\text{cm},\angle\text{F}=100^\circ$
  • C
    $\text{EF}=12\text{cm},\angle\text{D}=100^\circ$
  • D
    $\text{EF}=12\text{cm},\angle\text{D}=30^\circ$

Answer

Correct option: B.
$\text{DE}=12\text{cm},\angle\text{F}=100^\circ$
Given, $\triangle\text{ABC}\sim\triangle\text{DFE},$ $\text{then }\angle\text{A}=\angle{\text{D}}=30^\circ,\angle{\text{C}}=\angle{\text{E}}=50^\circ$

$\therefore\angle\text{B}=\angle\text{F}=180^\circ-(30^\circ+50^\circ)=100^\circ$
$\text{Also}, \text{AB}=5\text{cm},\text{AC}=8\text{cm}\text{ and}\text{ DF}=7.5\text{cm}$
$\therefore\frac{\text{AB}}{\text{DF}}=\frac{\text{AC}}{\text{DE}}$
$\Rightarrow\frac{5}{7.5}=\frac{8}{\text{DE}}$
$\therefore\text{DE}=\frac{8\times7.5}{5}=12\text{cm}$
$\text{Hence},\text{DE}=12\text{cm},\angle\text{F}=100^\circ$

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