Question : The perimeter of a triangle is 54 m and its sides are in the ratio of 5 : 6 : 7. The area of the triangle is:

Option 1: $18\ \text{m}^2$

Option 2: $54\sqrt6\ \text{m}^2$

Option 3: $27\sqrt2\ \text{m}^2$

Option 4: $25\ \text{m}^2$

Question : The sides of similar triangle $\triangle ABC$ and $\triangle DEF$ are in the ratio of $\frac{\sqrt{3}}{\sqrt{5}}$. If the area of $\triangle ABC$ is $90 \text{ cm}^2$, then the area of $\triangle DFF\left(\right.$ in $\left.\text{cm}^2\right)$ is:

Option 1: 150

Option 2: 152

Option 3: 154

Option 4: 156

Question : The distance between the centres of two circles of radii 6 cm and 3 cm is 15 cm. The length of the transverse common tangent to the circles is:

Option 1: $12\ \text{cm}$

Option 2: $6\sqrt6\ \text{cm}$

Option 3: $7\sqrt6\ \text{cm}$

Option 4: $18\ \text{cm}$

Question : What is the value of $\frac{\frac{5}{6} \text { of } \frac{1}{3} \times \frac{12}{25}-\frac{1}{3} \text { of } \frac{5}{6} \times \frac{18}{25}}{\frac{25}{12} \text { of } \frac{1}{6} \times \frac{2}{5}+\frac{3}{8} \text { of } \frac{12}{25} \times \frac{5}{6}}$?

Option 1: $-\frac{3}{13}$

Option 2: $-\frac{5}{13}$

Option 3: $-\frac{8}{25}$

Option 4: $-\frac{3}{25}$

Question : If the perimeter of an equilateral triangle is 18 cm, then the length of each median is:

Option 1: $3\sqrt2$ cm

Option 2: $2\sqrt3$ cm

Option 3: $3\sqrt3$ cm

Option 4: $2\sqrt2$ cm

Question : The perimeter of an isosceles triangle is 544 cm and each of the equal sides is $\frac{5}{6}$ times the base. What is the area (in cm²) of the triangle?

Option 1: 38172

Option 2: 18372

Option 3: 31872

Option 4: 13872