Question : $\triangle \mathrm {ABC}$ is similar to $\triangle \mathrm{PQR}$ and $\mathrm{PQ}=10 \mathrm{~cm}$. If the area of $\triangle \mathrm{ABC}$ is $32 \mathrm{~cm}^2$ and the area of $\triangle \mathrm{PQR}$ is $50 \mathrm{~cm}^2$, then the length of $A B$ (in $\mathrm{cm}$ ) is equal to:

Option 1: 10

Option 2: 4

Option 3: 6

Option 4: 8

Question : In $\triangle \mathrm{CAB}, \angle \mathrm{CAB}=90^{\circ}$ and $\mathrm{AD} \perp \mathrm{BC}$. If $\mathrm{AC}=24 \mathrm{~cm}, \mathrm{AB}=10 \mathrm{~cm}$. then find the value of $AD$ (in cm).

Option 1: 9.23

Option 2: 8.23

Option 3: 7.14

Option 4: 10.23

Question : In $\triangle $ABC, AD$\perp$ BC and AD² = BD × DC. The measure of $\angle$ BAC is:

Option 1: 60°

Option 2: 75°

Option 3: 90°

Option 4: 45°

Question : $\triangle \mathrm{ABC}$ is an isosceles triangle with $\angle \mathrm{ABC}=90^{\circ}$ and $\mathrm{AB}=\mathrm{BC}$. If $\mathrm{AC}=12 \mathrm{~cm}$, then the length of $\mathrm{BC}$ (in $\mathrm{cm}$) is equal to:

Option 1: $6 \sqrt{2}$

Option 2: $8$

Option 3: $6$

Option 4: $8 \sqrt{2}$

Question : AD is the median of $\triangle \mathrm{ABC}$. G is the centroid of $\triangle \mathrm{ABC}$. If AG = 14 cm, then what is the length of AD?

Option 1: 42 cm

Option 2: 28 cm

Option 3: 35 cm

Option 4: 21 cm