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:

Question : ABC is an isosceles right-angled triangle with $\angle$B = 90°. On the sides AC and AB, two equilateral triangles ACD and ABE have been constructed. The ratio of the area of $\triangle$ABE and $\triangle$ACD is:

Question : $\triangle\mathrm{ABC}$ is a right angled triangle. $\angle \mathrm{A}=90°$, $AB = 4$ cm, and $BC = 5$ cm. What is the value of $\cos B + \cot C$?

Question : If $\sin(A+B)=\sin A\cos B+\cos A \sin B$, then the value of $\sin75°$ is:

Question : Let $ABC$ and $PQR$ be two congruent right-angled triangles such that $\angle A=\angle P=90^{\circ}$. If $BC=13\ \text{cm}$ and $PR=12\ \text{cm}$, then find the length of $AB$.