Question : PQRS is a square with a side of 10 cm. A, B, C, and D are mid-points of PQ, QR, RS, and SP, respectively. Then, the perimeter of the square ABCD so formed is:

Option 1: $10\sqrt{2}\ \text{cm}$

Option 2: $20\sqrt{2}\ \text{cm}$

Option 3: $25\sqrt{2}\ \text{cm}$

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

Question : The length of the diagonals of a rhombus is 40 cm and 60 cm. What is the length of the side of the rhombus?

Option 1: $50 \sqrt{3} \ \text{cm}$

Option 2: $20 \sqrt{3}\ \text{cm}$

Option 3: $10 \sqrt{13}\ \text{cm}$

Option 4: $40 \sqrt{13}\ \text{cm}$

Question : The three sides of a triangle are 7 cm, 9 cm, and 8 cm. What is the area of the triangle?

Option 1: $12 \sqrt{3} \;\mathrm{Sq} . \mathrm{cm}$

Option 2: $10\sqrt{3} \;\mathrm{Sq} . \mathrm{cm}$

Option 3: $12 \sqrt{5} \;\mathrm{Sq} . \mathrm{cm}$

Option 4: $2 \sqrt{5} \;\mathrm{Sq} . \mathrm{cm}$

Question : The sides of a triangle are 9 cm, 6 cm, and 5 cm. What is the value of the circumradius of this triangle?

Option 1: $\frac{9 \sqrt{2}}{2} \mathrm{~cm}$

Option 2: $\frac{9 \sqrt{3}}{5} \mathrm{~cm}$

Option 3: $\frac{9 \sqrt{3}}{4} \mathrm{~cm}$

Option 4: $\frac{27 \sqrt{2}}{8} \mathrm{~cm}$

Question : The distance between the centres of two circles with radii of 9 cm and 16 cm is 25 cm. The length of the segment of the tangent between them is:

Option 1: $24\ \text{cm}$

Option 2: $25\ \text{cm}$

Option 3: $\frac{50}{3}\ \text{cm}$

Option 4: $12\ \text{cm}$