Question : The circumference of a circle is equal to the perimeter of an equilateral triangle. If the radius of the circle is 7 cm, what is the length of the side of the equilateral triangle?

Option 1: $\frac{22}{3}$ cm

Option 2: $\frac{44}{3}$ cm

Option 3: $44$ cm

Option 4: $22$ cm

Question : The length of the altitude of an equilateral triangle is $6 \sqrt{3}\;m$. The perimeter of the equilateral triangle (in m) is:

Option 1: $12 \sqrt{2}$

Option 2: $36 \sqrt{2}$

Option 3: $36$

Option 4: $24 \sqrt{3}$

Question : The length of a side of an equilateral triangle is 8 cm. The area of the region lying between the circumcircle and the incircle of the triangle is __________ ( Use: $\pi = \frac{22}{7}$)

Option 1: $50\frac{1}{7}\ \text{cm}^2$

Option 2: $50\frac{2}{7}\ \text{cm}^2$

Option 3: $75\frac{1}{7}\ \text{cm}^2$

Option 4: $75\frac{2}{7}\ \text{cm}^2$

Question : The side of an equilateral triangle is 9 cm. What is the radius of the circle circumscribing this equilateral triangle?

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

Option 2: $5\sqrt{3}$ cm

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

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

Question : In an isosceles triangle, the length of each equal side is twice the length of the third side. The ratios of areas of the isosceles triangle and an equilateral triangle with the same perimeter are:

Option 1: $30\sqrt{5}:{100}$

Option 2: $32\sqrt{5}:{100}$

Option 3: $36\sqrt{5}:{100}$

Option 4: $42\sqrt{5}:{100}$