# Choose the correct answer from the given four options:It is given that $\triangle \mathrm{ABC} \sim \triangle \mathrm{DFE}, \angle \mathrm{A}=30^{\circ}, \angle \mathrm{C}=50^{\circ}, \mathrm{AB}=5 \mathrm{~cm}, \mathrm{AC}=8 \mathrm{~cm}$ and $D F=7.5 \mathrm{~cm}$. Then, the following is true:(A) $\mathrm{DE}=12 \mathrm{~cm}, \angle \mathrm{F}=50^{\circ}$(B) $\mathrm{DE}=12 \mathrm{~cm}, \angle \mathrm{F}=100^{\circ}$(C) $\mathrm{EF}=12 \mathrm{~cm}, \angle \mathrm{D}=100^{\circ}$(D) $\mathrm{EF}=12 \mathrm{~cm}, \angle \mathrm{D}=30^{\circ}$

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Given:

$\triangle \mathrm{ABC} \sim \triangle \mathrm{DFE}, \angle \mathrm{A}=30^{\circ}, \angle \mathrm{C}=50^{\circ}, \mathrm{AB}=5 \mathrm{~cm}, \mathrm{AC}=8 \mathrm{~cm}$ and $D F=7.5 \mathrm{~cm}$.

To do:

We have to choose the correct answer.

Solution:

From the figure,

$\angle B=\angle F$

$=180^{\circ}-(30^{\circ}+50^{\circ})$

$=100^{\circ}$

$A B=5 \mathrm{~cm}, A C=8 \mathrm{~cm}$ and $DF=7.5 \mathrm{~cm}$

Therefore,

$\frac{A B}{D F}=\frac{A C}{D E}$

$\frac{5}{7.5}=\frac{8}{D E}$

$D E=\frac{8 \times 7.5}{5}$

$=12 \mathrm{~cm}$

Therefore,

$D E=12 \mathrm{~cm}, \angle F=100^{\circ}$

Updated on 10-Oct-2022 13:27:53