Question : The perimeter of a rectangle is 30 cm. If the length of the rectangle is twice its breadth, then what is the length of its diagonal?

Option 1: $5 \sqrt{5}\text{ cm}$

Option 2: $3 \sqrt{2} \text{ cm}$

Option 3: $4 \sqrt{5} \text{ cm}$

Option 4: $5 \sqrt{4} \text{ cm}$

Question : The perimeter of a rectangle is 40 cm. If its breadth is 8 cm, then what is the difference between the length and breadth of this rectangle?

Option 1: 3 cm

Option 2: 4 cm

Option 3: 5 cm

Option 4: 6 cm

Question : Nine times the area of a circle is the same as the three times the area of a square. What is the ratio of the diameter of the circle and the diagonal of the square?

Option 1: $\sqrt{2}: \sqrt{3 \pi}$

Option 2: $2: \sqrt{3 \pi}$

Option 3: $2: 3 \pi$

Option 4: $\sqrt{5}: \sqrt{7 \pi}$

Question : The larger diagonal of a rhombus is 150% of its smaller diagonal, and its area is 432 cm². Find the length (in cm) of the side of the rhombus.

Option 1: $8 \sqrt{13}$

Option 2: $4 \sqrt{13}$

Option 3: $6 \sqrt{13}$

Option 4: $2 \sqrt{13}$

Question : The ratio of the length to the width of a rectangle is 3 : 2. If the length of this rectangle is increased by 25% and its width is kept constant, then the area of the rectangle increases by 24 m². What is the width of this rectangle?

Option 1: 12 m

Option 2: 10 m

Option 3: 8 m

Option 4: 15 m