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 area of a square is 1296 cm² and the radius of a circle is $\frac{7}{6}$ of the length of a side of the square. What is the ratio of the perimeter of the square and the circumference of the circle? [Use $\pi=\frac{22}{7}$ ]

Option 1: 13 : 11

Option 2: 8 : 11

Option 3: 6 : 11

Option 4: 3 : 7

Question : The length of each side of a rhombus is 10 cm. If the length of one of its diagonals is 16 cm, then what is the area of the rhombus?

Option 1: 108 cm²

Option 2: 112 cm²

Option 3: 128 cm²

Option 4: 96 cm²

Question : The height of a trapezium is 68 cm, and the sum of its parallel sides is 75 cm. If the area of the trapezium is $\frac{6}{17}$ times of the area of a square, then the length of the diagonal of the square is: (Take $\sqrt{2}=1.41$ )

Option 1: 127.39 cm

Option 2: 183.49 cm

Option 3: 119.85 cm

Option 4: 102.39 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: $\sqrt{5}: \sqrt{7 \pi}$