Question : In $\triangle ABC$, AB = BC = $k$, AC =$\sqrt2k$, then $\triangle ABC$ is a:

Option 1: Isosceles triangle

Option 2: Right-angled triangle

Option 3: Equilateral triangle

Option 4: Right isosceles triangle

Question : $ABC$ is a right-angled triangle, right-angled at B and $\angle A=60°$ and $AB=20$ cm, then the ratio of sides $BC$ and $CA$ is:

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

Option 2:

$1:\sqrt{3}$

Option 3:

$\sqrt{3}:\sqrt{2}$

Option 4:

$\sqrt{3}:2$

Question : In $\triangle$ABC, BD and CE are perpendicular to AC and AB respectively. If BD = CE, then $\triangle$ABC is:

Option 1: Equilateral

Option 2: Isosceles

Option 3: Right–angled

Option 4: Scalene

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 : $\triangle \mathrm{ABC}$ is an isosceles triangle with $\angle \mathrm{ABC}=90^{\circ}$ and $\mathrm{AB}=\mathrm{BC}$. If $\mathrm{AC}=12 \mathrm{~cm}$, then the length of $\mathrm{BC}$ (in $\mathrm{cm}$) is equal to:

Option 1: $6 \sqrt{2}$

Option 2: $8$

Option 3: $6$

Option 4: $8 \sqrt{2}$