Question : The perimeter of two similar triangles is 30 cm and 20 cm, respectively. If one side of the first triangle is 9 cm. Determine the corresponding side of the second triangle.

Option 1: 13.5 cm

Option 2: 6 cm

Option 3: 15 cm

Option 4: 5 cm

Question : The perimeter of a certain isosceles right triangle is $10+10\sqrt{2}$ cm. What is the length of the Hypotenuse of the triangle?

Option 1: $5$ cm

Option 2: $10$ cm

Option 3: $5\sqrt{2}$ cm

Option 4: $10\sqrt{2}$ cm

Question : In ΔABC with sides 8 cm, 9 cm and 12 cm, the angle bisector of the largest angle divides the opposite sides into two segments. What is the length of the shorter segment?

Option 1: $5 \frac{11}{17} {~cm}$

Option 2: $4\frac{11}{17} {~cm}$

Option 3: $6\frac{13}{17} {~cm}$

Option 4: $3\frac{9}{17} {~cm}$

Question : The area of a square and rectangle are equal. The length of the rectangle is greater than the length of a side of the square by 10 cm and the breadth is less than 5 cm. The perimeter (in cm) of the rectangle is:

Option 1: 50

Option 2: 40

Option 3: 80

Option 4: 100

Question : A circle touches the side BC of a $\triangle A B C$ at P and also touches AB and AC produced at Q and R, respectively. If the perimeter of $\triangle A B C=26.4 \mathrm{~cm}$, then the length of AQ is:

Option 1: 17.6 cm

Option 2: 13.2 cm

Option 3: 15.4 cm

Option 4: 8.8 cm