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Triangles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTriangles1 Mark
MCQ
It is given that $\triangle A B C \sim \triangle D F E, \angle A=30^{\circ}, \angle C=50^{\circ}, A B=5 cm, A C=8 cm$ and $D F=7.5 cm$. Then, which of the following is true?
  • A
    $D E=12 cm, \angle F=50^{\circ}$
  • ✓
    $D E=12 cm, \angle F=100^{\circ}$
  • C
    $E F=12 cm, \angle D=100^{\circ}$
  • D
    $E F=12 cm, \angle D=30^{\circ}$
✓

Answer

Correct option: B.
$D E=12 cm, \angle F=100^{\circ}$
(B)$D E=12 cm, \angle F=100^{\circ}$
It is given that $\triangle A B C \sim \triangle D F E$.
$
\begin{array}{ll}
\therefore & \angle A=\angle D, \angle B=\angle F, \angle C=\angle E \text { and } \frac{A B}{D F}=\frac{B C}{E F}=\frac{A C}{D E} \\
\Rightarrow & \angle D=30^{\circ}, \angle F=100^{\circ}, \angle E=50^{\circ} \text { and } \frac{5}{7.5}=\frac{B C}{E F}=\frac{8}{D E} \quad\left[\because \angle A=30^{\circ}, \angle C=50^{\circ} \therefore \angle B=100^{\circ}\right] \\
\Rightarrow & \angle F=100^{\circ} \text { and } D E=12 cm .
\end{array}
$

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