If the incentre of an equilateral triangle lies inside the triangle and its radius is 3 cm, then the side of the equilateral triangle is

If ABC is an equilateral triangle and P, Q, R respectively denote the middle points of AB, BC, CA then.

Let ABC be an equilateral triangle and AX, BY, CZ be the altitudes. Then the right statement out of the four given responses is

If $${secθ+tanθ\over secθ-tanθ}={5\over 3}$$ then sinθ is equal to ;

If x = a secθ cos∅, y = b secθ sin∅, z=c tanθ, then the value of $$ {x^2\over a^2}+{y^2\over b^2}-{z^2\over c^2} $$

The length of a rectangular garden is 12 metres and its breadth is 5 metres. Find the length of the diagonal of a square garden having the same area as that of the rectangular garden:

A circular wire of diameter 42 cm is folded in the shape of a rectangle whose sides are in the ratio 6 : 5 . Find the area enclosed by the rectangle. (Take π = 22/7 ) 

The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is