A box of constant volume `c` is to be twice as long as it is wide. The material on the top and four sides cost three times as much per square metre as that in the bottom. What are the most economic dimensions?

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?

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 swimming pool is 20m long 15m wide and 3m deep. Find the cost of repairing the floor and wall at the rate of Rs. 25per square metre.

A table top is 9 dm 5 cm long 6 dm 5 cm broad. What will be the cost to polish it at the rate of 20 paise per square centimetre?

The volume of a closed square based rectangular box is 1000 cubic metre. The cost of constructing the base is 15 paise per square metre and the cost of constructing the top is 25 paise per square metre. The cost of constructing its sides is 20 paise per square metre and the cost of constructing the box is Rs. 3.Find the dimensions of box for minimum cost of construction.

A small, open-top packing box, similar to a shoebox without a lid, is three times as long as it is wide, and half as high as it is long. Each square inch of the bottom of the box costs $0.80 to produce, while each square inch of any side costs $0.03 to produce. If x represents the number of inches in the width of the box,which of the following functions represents the cost, C, of producing the box?

A room is in the shape of a square of side 4m. Calculate the area of the floor. What is the cost of tiling the floor at the rate of ₹ 24 per square metre?

A metal box with a square base and vertical sides is to contain 1024 cm3 of water, the material for the top and bottom costs Rs 5 per cm2 and the material for the sides costs Rs 2.50 per cm2. Find the least cost of the box.

If twice the area of a smaller square is subtracted from the area of a larger square, the result is 14 c m^2dot However, if twice the area of the larger square is added to three times the area of the smaller square, the result is 203 c m^2 . Determine the sides of the square.