1.A square field has an area of 6050 square meters. What is the length of its diagonal?
2.By what percentage does the area of a square increase if each side length is enlarged by 25%?
3.A rhombus has an area of 2016 square centimeters and each side measures 65 centimeters. What are the lengths of its diagonals?
4.What is the maximum possible area of a triangle that can be inscribed inside a semicircle with radius R cm?
5.A typist has a sheet of paper measuring 30 cm by 15 cm. He leaves margins of 2.5 cm at the top and bottom, and 12.5 cm on both the left and right sides. Approximately what percentage of the paper's total area remains available for typing?
6.Two triangles are similar, with areas measuring 12 cm² and 48 cm² respectively. If the height of the smaller triangle is 2.1 cm, what is the height of the larger triangle corresponding to it?
7.If the height of a triangle is reduced by 40% while its base is increased by 40%, how will the area of the triangle be affected?
8.The sides of a triangle are proportional to 1/2, 1/3, and 1/4. If the triangle's perimeter measures 52 cm, what is the length of its shortest side?
9.Given that a circle, a square, and an equilateral triangle all have the same area, which shape has the largest perimeter?
10.A rectangle with sides measuring 18 cm and 26 cm has the same perimeter as a circle. What is the area of that circle?
11.If the length of each side of a square is increased by 50%, what is the ratio of the new square's area to the original square's area?
12.If the length of a rectangle is increased by 20% while its width is reduced by 20%, what happens to its area?
13.If both the length and width of a rectangular garden are increased by 20%, what is the percentage increase in the garden's area?
14.If the length of a rectangular plot is increased by 25%, by what percentage should the width be adjusted to maintain the same area?
15.A rectangular field has a length that is double its width. If the total area of the field is 6075 square meters, what is the length of the field?
16.A rectangle and a square each have a perimeter of 160 meters. The rectangle's area is 100 square meters less than the area of the square. What is the length of the rectangle?
17.A square has a diagonal measuring 4√2 cm. If another square has an area twice as large as the first square, what is the length of the diagonal of this second square?
18.What is the maximum length of bamboo that can fit inside a square plot measuring 100 square meters?
19.A rectangle has an area of 12 square meters, and its length is three times its width. What is the perimeter of this rectangle?
20.A rectangle has a perimeter of 60 meters. If its length is double its width, what is the area of the rectangle?