Question : If $\triangle A B C \sim \triangle F D E$ such that $A B=9 \mathrm{~cm}, A C=11 \mathrm{~cm}, D F=16 \mathrm{~cm}$ and $D E=12 \mathrm{~cm}$, then the length of $BC$ is:

Option 1: $5 \frac{3}{4} \mathrm{~cm}$

Option 2: $4\frac{3}{5} \mathrm{~cm}$

Option 3: $3\frac{5}{7} \mathrm{~cm}$

Option 4: $6\frac{3}{4} \mathrm{~cm}$

Question : If $\triangle ABC \sim \triangle QRP, \frac{\operatorname{area}(\triangle A B C)}{\operatorname{area}(\triangle Q R P)}=\frac{9}{4}, A B=18 \mathrm{~cm}, \mathrm{BC}=15 \mathrm{~cm}$, then the length of $\mathrm{PR}$ is:

Option 1: 16 cm

Option 2: 14 cm

Option 3: 10 cm

Option 4: 12 cm

Question : In $\mathrm{\Delta ABC, \angle BAC = 90^{\circ}}$ and $\mathrm{AD}$ is drawn perpendicular to $\mathrm{BC}$. If $\mathrm{BD} = 7\;\mathrm{cm}$ and $\mathrm{CD }= 28\;\mathrm{cm}$, what is the length of $\mathrm{AD}$? 

Option 1: $3.5 \text{ cm}$

Option 2: $7 \text{ cm}$

Option 3: $10.5 \text{ cm}$

Option 4: $14 \text{ cm}$

Question : $\triangle \mathrm{ABC} \sim \triangle \mathrm{DEF}$ and the perimeters of these triangles are 32 cm and 12 cm, respectively. If $\mathrm{DE}=6 \mathrm{~cm}$, then what will be the length of AB?

Option 1: 16 cm

Option 2: 14 cm

Option 3: 12 cm

Option 4: 18 cm

Question : If $\mathrm{D}$ is the midpoint of $\mathrm{BC}$ in $\triangle \mathrm{ABC}$ and $\angle A=90^{\circ}$, then $AD=$ ______.

Option 1: $\frac{\mathrm{BC}}{4}$

Option 2: $2 \mathrm{BC}$

Option 3: $\frac{\mathrm{BC}}{2}$

Option 4: $\mathrm{BC}$