There is a square field with each side 500 meters long. It has a compound wall along its perimeter. At one of its corners, a triangular area of the field is to be cordoned off by erecting a straight line fence. The compound wall and the fence will form its borders. If the length of the fence is 100 meters, what is the maximum area in square meters that can be cordoned off?

There is a circle of radius 1 cm. Each member of a sequence of regular polygons Sl (n), n = 4, 5, 6.... where n is the number of sides of the polygon, is circumscribing the circle; and each member of the sequence of regular polygons S2 (n), n = 4, 5, 6..... where n is the number of sides of the polygon, is inscribed in the circle. Let L1(n) and L2(n) denote the perimeters of the corresponding polygons of S1 (n) and S2 (n). Then {L1(13)+2π}/L2(17) is

The resistance of a wire is proportional to its length and inversely proportional to the square of its radius. Two wires of the same material have the same resistance and their radii are in the ratio 9 : 8. If the length of the first wire is 162 cms., find the length of the other.