Question : If the measures of the angles of a triangle are in the ratio 1 : 2 : 3, and if the length of the smallest side of the triangle is 10 cm, then the length of the longest side is:

Option 1: 20 cm

Option 2: 25 cm

Option 3: 30 cm

Option 4: 35 cm

Question : $\triangle ABC \sim \triangle DEF$ such that AB = 9.1 cm and DE = 6.5 cm. If the perimeter of $\triangle DEF = 25$ cm, then the perimeter of $\triangle ABC$ is:

Option 1: 40 cm

Option 2: 30 cm

Option 3: 35 cm

Option 4: 45 cm

Question : The ratio of the length of each equal side and the third side of an isosceles triangle is 3 : 5. If the area of the triangle is $30 \sqrt{11}$ cm², then the length of the third side (in cm) is:

Option 1: $10\sqrt{6}$

Option 2: $5\sqrt{6}$

Option 3: $13\sqrt{6}$

Option 4: $11\sqrt{6}$

Question : The sides of a triangle are in the ratio $\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$ and its perimeter is 104 cm. The length of the longest side (in cm) is:

Option 1: 52

Option 2: 48

Option 3: 32

Option 4: 26

Question : $\triangle PQR$ is right-angled at $Q$. The length of $PQ$ is 5 cm and $\angle P R Q=30^{\circ}$. Determine the length of the side $QR$.

Option 1: $5 \sqrt{3}~cm$

Option 2: $3 \sqrt{3}~cm$

Option 3: $\frac{1}{\sqrt{3}}~cm$

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