Question : The perimeter of two similar triangles is 30 cm and 20 cm, respectively. If one side of the first triangle is 9 cm. Determine the corresponding side of the second triangle.

Option 1: 13.5 cm

Option 2: 6 cm

Option 3: 15 cm

Option 4: 5 cm

Question : The radius of the incircle of a triangle is 2 cm. If the area of the triangle is 6 cm², then its perimeter is:

Option 1: 2 cm

Option 2: 3 cm

Option 3: 6 cm

Option 4: 9 cm

Question : The sides of a triangle are 8 cm, 12 cm, and 16 cm. What is the area of the triangle?

Option 1: $24 \sqrt{15}~\text{cm}^2$

Option 2: $6 \sqrt{15}~\text{cm}^2$

Option 3: $8 \sqrt{15}~\text{cm}^2$

Option 4: $12 \sqrt{15}~\text{cm}^2$

Question : Let $\triangle ABC \sim \triangle RPQ$ and $\frac{{area}(\triangle {ABC})}{{area}(\triangle {PQR})}=\frac{4}{9}$. If AB = 3 cm, BC = 4 cm and AC = 5 cm, then RP (in cm) is equal to:

Option 1: 6

Option 2: 5

Option 3: 4.5

Option 4: 12

Question : $P Q R S$ is a rectangle. $T$ is a point on $P Q$ such that $R T Q$ is an isosceles triangle and $P T=5 \mathrm{QT}$. If the area of triangle RTQ is $12 \sqrt{3}$ sq.cm, then the area of the rectangle PQRS is:

Option 1: $144 \sqrt{3}$ sq.cm

Option 2: $142$ sq. cm

Option 3: $134 \sqrt{3}$ sq. cm

Option 4: $142\sqrt{3}$ sq. cm