The area of a circle inscribed in an equilateral triangle is $36\mathrm{\pi }$ $sq units$. The length of altitude of triangle is:

Read the given question and decide which of the following information is sufficient to answer the question.

What is the value of 0?

Information :

(II) 0 < q < 90°

In the given diagram, point R and Q are on PS. ÐPQT = x°, ÐRQT = (x – 50)° and ÐTUR = (x + 25°). find the value of ÐURS.

$5 : 18$ is the ratio of the length and perimeter of a rectangle. What would be the ratio of its length and breadth?

The two circles with radii $6 cm$ and $3 cm$ centred at the point $P$ and $Q$ respectively. A transverse common tangent $AC$ to the both circles cuts line Joining $P$ and $Q$ at the point $B$ such that $AB = 8 cm$. Calculate the length (in cm.) of $PQ$.

If the interior angle of a regularpolygon is $108°$, then it is a-

1. Octagon

2. Hexagon

3. Pentagon

4. Tetragon 

$\mathrm{ABC}$ is an equilateral triangle of side $2\mathrm{a}$, then length of one of its altitude is $a\sqrt{x}$. The value of $\mathrm{a}$ is _____.