1.A rectangle has a length that is double its width. If the length is reduced by 5 cm and the width is increased by 5 cm, what is the length of the rectangle?
2.A rectangle has a length of 15 cm and an area of 159 cm². If the area is increased to 1⅓ times the original by extending only the length, what is the new perimeter of the rectangle?
3.A rectangular room has a length of 4 meters. If it is divided into two identical square rooms, what is the length of each side of these square partitions in meters?
4.If the side length of a square is increased by 40% and its width is increased by 30%, by what percentage does the area of the new rectangle surpass the original square's area?
5.A rectangular hall measures 20 meters in length and 15 meters in width. It is enclosed by a verandah of consistent width measuring 2.5 meters. What is the total cost of flooring the verandah if the rate is Rs. 3.50 per square meter?
6.Given that the areas of two squares are in the ratio 9 to 1, what is the ratio of their perimeters?
7.If the length of a rectangle is increased by 60%, by what percentage must the width be reduced to keep the area unchanged?
8.A rectangle's area is three times larger than that of a square. The rectangle's length measures 40 cm, and its width is 1.5 times the side length of the square. What is the length of the square's side in centimeters?
9.A hall's length is (4/3) times its width. If the total area of the hall is 300 square meters, what is the difference between its length and width?
10.If the length of each side of a square is increased by 25%, by what percentage does its area increase?
11.The length and width of a rectangular plot are in the ratio 5:4. If the width is 20 meters shorter than the length, what is the perimeter of the plot?
12.A rectangular plot has its length and width in the ratio 5:3. If the owner spends Rs 3000 to fence the entire plot at a cost of Rs 7.50 per meter, what is the difference between the length and the width of the plot?
13.A playground measures 36 meters in length and 21 meters in width. Flagpoles need to be installed all around the boundary, spaced 3 meters apart. How many flagpoles are required in total?
14.A plot's length is four times its width. A playground covering 1200 square meters takes up one-third of the entire plot's area. What is the length of the plot in meters?
15.Given that the diagonal AC of square ABCD measures 5.2 cm, what is the area of the square?
16.In a circle with a radius of 5 cm, two equal chords AB and AC each measure 6 cm. What is the length of the chord BC?
17.A large rectangular land plot with an area of 4320 square meters is initially divided into three smaller square plots by fencing parallel to its shorter side. However, a leftover area remains that cannot form a square. To cover this remaining area completely, three additional square plots are created by fencing parallel to the longer side of the original plot. After this, no land area is left unused. What are the dimensions of the original rectangular plot?
18.Which shape among the following has the largest perimeter?
19.What is the area of a sector in a circle with a radius of 12 meters and a central angle of 42°?
20.What is the area of a sector in a circle with a radius of 5 cm if the length of the arc is 3.5 cm?