Question : The ratio of the sides of a triangle is 3 : 3 : 4. If the area of a triangle is $32 \sqrt{5}$ cm², then what is the length of the equal sides?

Option 1: 12 cm

Option 2: 16 cm

Option 3: 10 cm

Option 4: 15 cm

Question : The longest side of the obtuse triangle is 7 cm and the other two sides of the triangle are 4 cm and 5 cm. Find the area of the triangle.

Option 1: $1 \sqrt{3} \mathrm{~cm}^2$

Option 2: $6 \sqrt{3} \mathrm{~cm}^2$

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

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

Question : The lengths of the three sides of a triangle are in the ratio of 2 : 2 : 3. If the perimeter of the triangle is 42 cm, then what is the length of the largest side?

Option 1: 12 cm

Option 2: 18 cm

Option 3: 20 cm

Option 4: 15 cm

Question : The larger diagonal of a rhombus is 150% of its smaller diagonal, and its area is 432 cm². Find the length (in cm) of the side of the rhombus.

Option 1: $8 \sqrt{13}$

Option 2: $4 \sqrt{13}$

Option 3: $6 \sqrt{13}$

Option 4: $2 \sqrt{13}$

Question : The radius of the incircle of a triangle whose sides are 9 cm, 12 cm, and 15 cm is:

Option 1: 9 cm

Option 2: 13 cm

Option 3: 3 cm

Option 4: 6 cm