Question : The perimeter of the triangle is 67 cm. The first side is twice the length of the second side. The third side is 11 cm more than the second side. Find the length of the shortest side of the triangle.

Option 1: 12 cm

Option 2: 14 cm

Option 3: 17 cm

Option 4: 25 cm

Question : One side of the triangle is 15 cm and the corresponding height is 6 cm, then area of the triangle is:

Option 1: 46 sq. cm

Option 2: 45 sq. cm

Option 3: 47 sq. cm

Option 4: 48 sq. cm

Question : What is the area of a triangle having a perimeter of 32 cm, one side of 11 cm, and the difference between the other two sides is 5 cm?

Option 1: $8\sqrt{30}$ cm²

Option 2: $5\sqrt{35}$ cm²

Option 3: $6\sqrt{30}$ cm²

Option 4: $8\sqrt{2}$ cm²

Question : The radius of the incircle of a triangle is 2 cm. If the area of the triangle is 6 cm², then its perimeter is:

Option 1: 2 cm

Option 2: 3 cm

Option 3: 6 cm

Option 4: 9 cm

Question : The perimeters of two similar triangles are 36 cm and 24 cm, respectively. Find the ratio of their areas.

Option 1: 6 : 13

Option 2: 2 : 3

Option 3: 9 : 4

Option 4: 35 : 24