Planimetrics + prime numbers - practice problems
Number of problems found: 55
- Planetary system
Robert has built a mechanical model solar system with three balls representing planets at the end of rods. Each rod is attached to the center, representing the Sun. The planets are lined up when he turns on the motor. The innermost planet makes a revoluti - Paper
The drawing paper has dimensions 220mm and 308mm. Pupils should cut it into squares of the same size so that they are as large as possible. Determine the dimensions of the square in cm and the number of squares. - Jackie 2
Jackie bought an equal number of tulip bulbs and daffodil bulbs. Along the length of her garden, Jackie planted 6 daffodil bulbs and 3 tulip bulbs per foot. She has 5 daffodil bulbs and 29 tulip bulbs remaining to plant elsewhere. How long is Jackie's gar - Dimensions 6201
Mr. John's plot of land has dimensions of 252 dm and 28 m. How far apart must he place the fence posts, so they are the same distance on both sides? How many will he need to fence the entire property?
- Determine 36601
The plumbers have to cut sheet metal measuring 220 cm and 308 cm into squares of equal size so that the squares are as large as possible and the sheet metal is used without residue. How many such squares will they cut? Determine the side of this square. - Pexeso
Drawing paper has dimensions of 60cm and 840mm. Pupils have to divide it into squares to make a pexeso. What dimension must squares have if their side is larger than 3cm and less than 10cm? - Around the flowerbed
Around a rectangular flowerbed with dimensions 5.25 m and 3.5 m are to be planted roses equally spaced so that the roses are found in every corner of the flowerbed and consumed as little as possible. a) At what distance are planted roses? b) How many rose - Tractor wheels
The tractor's front wheel has a circumference of 18 dm and the rear 60 dm. We will make a red mark on the lowest point of both wheels. The tractor then starts. At what distance from the start will both marks appear identically at the bottom again? - The land
The owner wants to divide the land with dimensions of 220 m and 308 m into equally large square plots with the largest possible area. How long will one side of the plot be?
- Rectangle-shaped 80074
Pupils had to stack rectangle-shaped pictures with dimensions of 210mm and 84mm so as to cover the square. What is the smallest square we can cover like this, and how many images do we need? - Three 205
Three metallic bars of lengths 400 cm, 600 cm, and 720 cm are cut into equal pieces. Find the largest possible area of a square that can be made from any of the three bars. - Returning 27121
Two gears – one smaller and one larger rotate so that the teeth of both wheels mesh together. The first wheel has 18 teeth, the second 27. How often does each wheel turn before returning to its starting position? - Cutting paper
Divide a rectangular paper with dimensions 220mm and 308mm into squares of the same size so that they are as large as possible. Specify the length of the side of the square. - Dimensions 7131
The paper has dimensions 220mm and 308mm. We need to cut it into as large a square as possible. What will be the side of this square?
- Maximally 4036
Mr. Novák wants to pave the terrace with tiles of two sizes to be as small as possible. Its terrace is square with a side 3 meters long. There is a wall of the house on two sides of the terrace. Next to the wall, he wants to put small tiles, the rest larg - Square tiles
The room has dimensions of 12 meters and 5.6 meters. Determine the number of square tiles and their largest dimension to exactly cover the floor. - Smallest 44681
What is the smallest width of the pool to be divided without rest into equally wide tracks, either 80cm or 1m, or 120cm? - Rectangular 82582
We have to pave the smallest possible square with rectangular tiles with 168 cm and 280 cm sides. What will its side of the square be? - Rectangular 22761
We will pave a square plot of land from rectangular tiles with 25 cm and 30 cm dimensions. What is the smallest square plot we can pave with these tiles without cutting them?
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