A running track of 440 ft is to be laid out enclosing a football field the shape of which is a rectangle with a semi circle at each end .If the area of the rectangular portion is to be maximum then find the lengths of its sides.

A window is in the shape of a rectangle surmounted by a semi circle. If the perimeter of the window is of fixed length k then the maximum area of the window is

The inside perimeter of a running track (shown in figure) is 400m. The length of each of the straight portion is 90m and the ends are semi-circles. If the track is everywhere 14m wide, find the area of the track. Also find the length of the outer running track.

The inside perimeter of a running track (shown in figure) is 400m. The length of each of the straight portion is 90m and the ends are semi-circles. If track is everywhere 14m wide, find the area of the track. Also, find the length of the outer running track.

The inner perimeter of a running track (shown in figure) is 400 m. The length of each of the straight portion is 90 m and the ends are semicircular. If the track is everywhere 14 m wide, find the area of the track. Also, find the length of the outer running track.

The perimeter of a rectangular field is 3/(5) km. If the length of the field is twice its width, find the area of the rectangle in sq. metres.

The length of a rectangle is twice the side of a square and its width is 6 cm greater than the side of the square. If area of the rectangle is three times the area of the square, find the dimensions of each.

A rectangle is inscribed in a semi-circle of radius r with one of its sides on diameter of semi-circle. Find the dimensions of the rectangle so that its area is maximum. Find also the area.

A rectangle is inscribed in a semi-circle of radius r with one of its sides on diameter of semi-circle. Find the dimensions of the rectangle so that its area is maximum. Find also the area.

The perimeter of a rectangular field is 216 metres and its breadth is 40 metres . Find the length and area of the rectangle.

A window of perimeter P (including the base of the arch) is in the form of a rectangle surrounded by a semi-circle. The semi-circular portion is fitted with the colored glass while the rectangular part is fitted with the clear glass that transmits three times as much light per square meter as the colored glass does. What is the ratio for the sides of the rectangle so that the window transmits the maximum light?