1.A room is being floored at a rate of Rs. 8.50 per square meter, and the total flooring cost amounts to Rs. 510. If the room's length measures 8 meters, what is its width?
2.If the length of a rectangle is increased by 10% and its width is reduced by 10%, what is the percentage change in the area of the new rectangle?
3.A chessboard consists of 64 small squares with a total area of 400 cm². If there is a border 3 cm wide surrounding the entire board, what is the length of one side of the chessboard including the border?
4.A rectangular field measures 38 meters in length and 32 meters in width. A uniform path runs along the inside perimeter of the field, covering an area of 600 square meters. What is the width of this path?
5.What length of carpet, 63 cm wide, is needed to cover the floor of a room measuring 14 meters by 9 meters?
6.A rectangle has a length of 8 cm and its diagonal measures 10 cm. What is the perimeter of this rectangle?
7.A room has a floor perimeter measuring 18 meters and a wall height of 3 meters. What is the total surface area of the four walls?
8.A rectangular courtyard measures 3.78 meters in length and 5.25 meters in width. It is to be completely covered with square tiles of identical size without cutting any tile. What is the smallest number of tiles needed to cover the courtyard exactly?
9.A room measures 12.25 meters in length and 7 meters in width. What is the largest possible side length of a square tile (in centimeters) that can exactly cover the floor without cutting any tiles?
10.A rectangular rug covers an area of 120 square meters and has a perimeter measuring 46 meters. What is the length of its diagonal?
11.The length and breadth of a rectangular plot are in the ratio 3:2. If the breadth is 40 meters shorter than the length, what is the perimeter of the plot?
12.A rectangular field has a length that is 4.5 times its width. If the total area of the field is 200 square meters, what is the length of the field?
13.A rectangular carpet covers an area of 60 square meters. The sum of its diagonal and the longer side is five times the length of the shorter side. What is the length of the carpet?
14.A rectangular carpet measures 120 square meters in area and has a perimeter of 46 meters. What is the length of its diagonal?
15.A parallelogram has two sides measuring 60 meters and 40 meters, and one of its diagonals is 80 meters in length. What is the area of the parallelogram?
16.When a square and a rhombus share the same base length, what is the ratio of the area of the square to that of the rhombus?
17.A rhombus has an area of 144 square centimeters, and one diagonal is twice the length of the other. What are the lengths of the diagonals?
18.What should be the length of the rope to which a cow is tied so that it can graze an area of 9856 square meters?
19.Two concentric circles have circumferences measuring 176 meters and 132 centimeters. What is the difference in their radii?
20.The diameter of a circle is 105 cm shorter than its circumference. What is the length of the diameter?