The maximum area of the rectangle whose sides pass through the vertices of a given rectangle of sides `aa n db` is (a)`2(a b)` (b) `1/2(a+b)^2` (c)`1/2(a^2+b^2)` (d) `non eoft h e s e`

The maximum area of the triangle whose sides a,b and c satisfy 0leqaleq1,1leqbleq2 and 2leqcleq3 is

The largest area of a rectangle which has one side on the x-axis and the two vertices on the curve y=e^(-x^(2) is

The length and breadth of a rectangle of area A are doubled. The area of the new rectangle is (a) 2A (b) A^2 (c) 4 A (d) None of these

In Triangle A B C with fixed length of B C , the internal bisector of angle C meets the side A B a tD and the circumcircle at E . The maximum value of C D×D E is c^2 (b) (c^2)/2 (c) (c^2)/4 (d) none of these

A B C D is a square of unit area. A circle is tangent to two sides of A B C D and passes through exactly one of its vertices. The radius of the circle is (a) 2-sqrt(2) (b) sqrt(2)-1 (c) sqrt(2)-1/2 (d) 1/(sqrt(2))

A wire is in the form of a square of side 18 m . It is bent in the form of a rectangle, whose length and breadth are in the ratio 3: 1. The area of the rectangle is (a) 81\ m^2\ (b) 243 m^2 (c) 144 m^2 (d) 324 m^2

If A is the area and 2s is the sum of the sides of a triangle, then Alt=(s^2)/4 (b) Alt=(s^2)/(3sqrt(3)) 2RsinAsinBsinC (d) non eoft h e s e

The perimeter P of a rectangle of sides l\ a n d\ b is given by P=2\ (l+b)dot\ evaluate the variable and constant part

A rectangle of the greatest area is inscribed in a trapezium A B C D , one of whose non-parallel sides A B is perpendicular to the base, so that one of the rectangles die lies on the larger base of the trapezium. The base of trapezium are 6cm and 10 cm and A B is 8 cm long. Then the maximum area of the rectangle is 24c m^2 (b) 48c m^2 36c m^2 (d) none of these

In Figure, A B C D is a rectangle with sides A B=10 c m\ a n d\ A D=5c mdot Find the area of E F G