Question : In a right-angled triangle $\triangle$DEF, if the length of the hypotenuse EF is 12 cm, then the length of the median DX is:

Option 1: 3 cm

Option 2: 4 cm

Option 3: 6 cm

Option 4: 12 cm

Question : In a right-angled triangle, the product of two sides is equal to half of the square of the third side, i.e. the hypotenuse. One of the acute angles must be:

Option 1: 60°

Option 2: 30°

Option 3: 45°

Option 4: 15°

Question : In a right-angled triangle, if the hypotenuse is 20 cm and the ratio of the other two sides is 4 : 3, the lengths of the sides are:

Option 1: 4 cm and 3 cm

Option 2: 8 cm and 6 cm

Option 3: 12 cm and 9 cm

Option 4: 16 cm and 12 cm

Question : Suppose $\triangle ABC$ be a right-angled triangle where $\angle A=90°$ and $AD\perp BC$. If the area of $\triangle ABC =40$ cm$^{2}$ and $\triangle ACD =10$ cm$^{2}$ and $\overline{AC}=9$ cm, then the length of $BC$ is:

Option 1: 12 cm

Option 2: 18 cm

Option 3: 4 cm

Option 4: 6 cm

Question : In a right-angled triangle $\Delta PQR, PR$ is the hypotenuse of length 20 cm, $\angle PRQ = 30^{\circ}$, the area of the triangle is:

Option 1: $50\sqrt{3}\text{ cm}^{2}$

Option 2: $100\sqrt{3}\text{ cm}^{2}$

Option 3: $25\sqrt{3}\text{ cm}^{2}$

Option 4: $\frac{100}{\sqrt{3}}\text{ cm}^{2}$