Question : Possible lengths of the three sides of a triangle are:

Option 1: 2 cm, 3 cm, and 6 cm

Option 2: 3 cm, 4 cm, and 5 cm

Option 3: 2.5 cm, 3.5 cm, and 6 cm

Option 4: 4 cm, 4 cm, and 9 cm

Question : The lengths of the three medians of a triangle are $9\;\mathrm{cm}$, $12\;\mathrm{cm}$, and $15\;\mathrm{cm}$. The area (in $\mathrm{cm^2}$) of the triangle is:

Option 1: $24$

Option 2: $72$

Option 3: $48$

Option 4: $144$

Question : The three sides of a triangle are 5 cm, 9 cm, and x cm. The minimum integral value of x is:

Option 1: 2

Option 2: 3

Option 3: 4

Option 4: 5

Question : Let $0<x<1$. Then the correct inequality is:

Option 1: $x<\sqrt{x}<x^{2}$

Option 2: $\sqrt{x}<x<x^{2}$

Option 3: $x^{2}<x<\sqrt{x}$

Option 4: $\sqrt{x}< x^{2}<x$

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