Question : The diagonal of the square is $8 \sqrt{2}$ cm. Find the diagonal of another square whose area is triple that of the first square.

Option 1: $8 \sqrt{5}$ cm

Option 2: $8 \sqrt{3}$ cm

Option 3: $8 \sqrt{2}$ cm

Option 4: $8 \sqrt{6}$ cm

Question : In a triangle ${ABC}, {AB}={AC}$ and the perimeter of $\triangle {ABC}$ is $8(2+\sqrt{2}) $ cm. If the length of ${BC}$ is $\sqrt{2}$ times the length of ${AB}$, then find the area of $\triangle {ABC}$.

Option 1: $32 \ cm^2$

Option 2: $28 \ cm^2$

Option 3: $16 \ cm^2$

Option 4: $36 \ cm^2$

Question : $AB$ and $AC$ are the two tangents to a circle whose radius is 6 cm. If $\angle BAC=60^{\circ}$, then what is the value (in cm) of $\sqrt{\left ( AB^{2}+AC^{2} \right )}?$ 

Option 1: $6\sqrt{6}$

Option 2: $4\sqrt{6}$

Option 3: $9\sqrt{3}$

Option 4: $8\sqrt{3}$

Question : The area of the parallelogram whose length is 30 cm, width is 20 cm and one diagonal is 40 cm is:

Option 1: $200\sqrt{15}\text{ cm}^{2}$

Option 2: $100\sqrt{15}\text{ cm}^{2}$

Option 3: $300\sqrt{15}\text{ cm}^{2}$

Option 4: $150\sqrt{15}\text{ cm}^{2}$

Question : In $\triangle$LMN, LM = $5\sqrt{2}$ cm, LN = 13 cm and $\angle$LMN=135$^{\circ}$. What is the length (in cm) of MN?

Option 1: $7$

Option 2: $8$

Option 3: $8\sqrt{2}$

Option 4: $7\sqrt{2}$