Question : What is the area of a triangle whose sides are of lengths 12 cm, 13 cm and 5 cm?

Option 1: $30 \, \text{cm}^2$

Option 2: $15 \, \text{cm}^2$

Option 3: $40 \, \text{cm}^2$

Option 4: $70 \, \text{cm}^2$

Question : If each side of an equilateral triangle is 12 cm, then its altitude is equal to:

Option 1: $6 \sqrt{3}\ \text{cm}$

Option 2: $3 \sqrt{6}\ \text{cm}$

Option 3: $6 \sqrt{2}\ \text{cm}$

Option 4: $3 \sqrt{2}\ \text{cm}$

Question : In triangle ABC which is equilateral. O is the point of intersection of altitude AL, BM, and CN. If OA = 16 cm, what is the semi-perimeter of the triangle ABC?

Option 1: $8 \sqrt 3$ cm

Option 2: $12 \sqrt 3$ cm

Option 3: $16 \sqrt 3$ cm

Option 4: $24\sqrt 3$ 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 ratio of three sides of a triangle is $5: 5: 8$. If the area of triangle is $12\;\mathrm{cm^2}$, then what is the length (in$\;\mathrm{cm}$) of the equal sides?

Option 1: 5

Option 2: 8

Option 3: 6

Option 4: 2.5