Question : In $\triangle$ABC, $\angle$A = $\angle$B = 60°, AC = $\sqrt{13}$ cm, the lines AD and BD intersect at D with $\angle$D = 90°. If DB = 2 cm, then the length of AD is:

Option 1: 3 cm

Option 2: 3.5 cm

Option 3: 4 cm

Option 4: 4.7 cm

Question : If $\tan(A+B)=\sqrt{3}$, and $\tan(A-B)=\frac{1}{\sqrt{3}}$, $\angle A+\angle B<90°$; $A\geq B$ then $\angle A$ is:

Option 1: 90°

Option 2: 30°

Option 3: 45°

Option 4: 60°

Question : Two similar triangles are given i.e. $\triangle$LMN ~ $\triangle$PQR, with measurement of angle and side as $\angle$ L = 40°, $\angle$ N = 80°, LM = 6 cm, LN = 8 cm and PQ = 7.5 cm. Find the value of $\angle$ Q and side PR, respectively.

Option 1: 60° and 20 cm

Option 2: 50° and 6.5 cm

Option 3: 40° and 10 cm

Option 4: 60° and 10 cm

Question : If the length of the side of an equilateral triangle is 8 cm, what is its area (in cm²)?

Option 1: $32\sqrt{3}$

Option 2: $16$

Option 3: $16\sqrt{3}$

Option 4: $32$

Question : In an equilateral triangle STU, inradius is $5 \sqrt{3 }\mathrm{~cm}$. What is the length of the side of this equilateral triangle?

Option 1: $20 \sqrt{3} \mathrm{~cm}$

Option 2: $18 \sqrt{3} \mathrm{~cm}$

Option 3: $30 \mathrm{~cm}$

Option 4: $24 \mathrm{~cm}$