Question : The breadth ‘b’ of a room is twice its height and half of its length. Find the length of the longest diagonal of the room.

Option 1: $\frac{\sqrt{20} \mathrm{~b}}{2}$

Option 2: $\frac{\mathrm{b}}{2}$

Option 3: $\frac{\sqrt{21} \mathrm{~b}}{2}$

Option 4: $\frac{\sqrt{19} \mathrm{~b}}{2}$

Question : The length of each side of a triangle is 12 cm. What is the length of the circumradius of the triangle?

Option 1: $8 \sqrt{3} \mathrm{~cm}$

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

Option 3: $6 \sqrt{3} \mathrm{~cm}$

Option 4: $4 \sqrt{3} \mathrm{~cm}$

Question : Find the area of an equilateral triangle whose sides are 16 cm.

Option 1: $60\sqrt{3}\mathrm{~cm}^2$

Option 2: $62\sqrt{3} \mathrm{~cm}^2$

Option 3: $64\sqrt{3} \mathrm{~cm}^2$

Option 4: $66\sqrt{3} \mathrm{~cm}^2$

Question : If the side of an equilateral triangle is 16 cm, then what is its area?

Option 1: $81 \sqrt{3} \mathrm{~cm}^2$

Option 2: $48 \sqrt{3} \mathrm{~cm}^2$

Option 3: $32 \sqrt{3} \mathrm{~cm}^2$

Option 4: $64 \sqrt{3} \mathrm{~cm}^2$

Question : The perimeter of an equilateral triangle is 48 cm. Find its area (in cm²).

Option 1: $81\sqrt{3}$

Option 2: $8\sqrt{3}$

Option 3: $25\sqrt{3}$

Option 4: $64\sqrt{3}$