Question : If the hypotenuse of an isosceles right-angled triangle is 10 cm, then the other two sides (in cm) are __________.

Option 1: $10\sqrt{2}$ and $10\sqrt{2}$

Option 2: $8\sqrt{2}$ and $8\sqrt{2}$

Option 3: $6\sqrt{2}$ and $6\sqrt{2}$

Option 4: $5\sqrt{2}$ and $5\sqrt{2}$

Question : The perimeter of a right triangle is 60 cm and its hypotenuse is 26 cm. What is the area (in cm²) of the triangle?

Option 1: 60

Option 2: 96

Option 3: 90

Option 4: 120

Question : Find the area of a triangle whose length of two sides are 4 cm and 5 cm and the angle between them is 45°.

Option 1: $4 \sqrt{2} \mathrm{~cm}^2$

Option 2: $7 \sqrt{2} \mathrm{~cm}^2$

Option 3: $5 \sqrt{2} \mathrm{~cm}^2$

Option 4: $6 \sqrt{2} \mathrm{~cm}^2$

Question : What is the area of a triangle having a perimeter of 32 cm, one side of 11 cm, and the difference between the other two sides is 5 cm?

Option 1: $8\sqrt{30}$ cm²

Option 2: $5\sqrt{35}$ cm²

Option 3: $6\sqrt{30}$ cm²

Option 4: $8\sqrt{2}$ cm²

Question : In triangle ABC which is equilateral. O is the point of intersection of altitude AL, BM, and CN. If OA = 16 cm, what is the semi-perimeter of the triangle ABC?

Option 1: $8 \sqrt 3$ cm

Option 2: $12 \sqrt 3$ cm

Option 3: $16 \sqrt 3$ cm

Option 4: $24\sqrt 3$ cm