Planimetrics + divisibility - practice problems
Number of problems found: 27
- 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? - 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? - 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. - Matches
George poured out-of-the-box matches and composed their triangles, and no match was left. Then he tried squares, hexagons, and octagons, and no match was left. How many matches must be at least in the box? - Square room
What is the size of the smallest square room, which can be paved with tiles with dimensions of 55 cm and 45 cm? How many such tiles are needed? - Tiles
The tile has the shape of a square with a side of 15 cm. What dimensions can a rectangle composed of 90 tiles have so that no tile remains? - Gardens colony
The garden's colony, with dimensions of 180 m and 300 m, is to be completely divided into the same large squares of the highest area. Calculate how many such squares can be obtained and determine the length of the square side.
- Plumber
The plumber had to cut the metal strip with dimensions of 380 cm and 60 cm to the largest squares to no waste. Calculate the length of the sides of a square. How many squares cut it? - Pagans
Elena cut out the same circle-shaped pagans and put them on a rectangular sheet so that the neighboring pagans were touching each other and the pagans were touching the walls of the sheet on the edges. Each pagan occupied 28.26 cm² of the bottom of the sh - Measuring 26891
What is the smallest square space we can tile with tiles measuring 25 x 15 cm, knowing there will be no need to cut them? How many tiles will we use? - Tiles
From how many tiles, 20 cm by 30 cm, we can build a square of maximum dimensions if we have maximum 275 tiles. - Tiles
Hall has dimensions 250 × 200 dm. What is the largest size of square tiles that can be entire hall tiled, and how many do we need them?
- Tiles
It is given an area of 5m x 4m. One tile is 40 x 40 cm. How many tiles are needed in an area of 5 m x 4 m? And how many tiles need to be cut (if the tiles can't fall exactly)? - Paper squares
We should cut the paper rectangle measuring 69 cm and 46 cm into as many squares as possible. Calculate the lengths of squares and their number. - Circumference of the garden
The garden is 90 m long. What is the smallest width if it is possible to walk (circumference) in steps of 80 cm or 50 cm? - The carpet
How many meters of carpet 90 cm wide need to cover the floor room, which has a rectangular shape with lengths of 4.8 m and 2.4 m, if the number of pieces on the carpet is needed to be lowest? - Snowman 2
On the medal, which has the shape of a circle with a diameter 18 cm, is sketched a snowman so that the following requirements are met: 1. snowman is composed of three circles, 2. space over the snowman is the same as under it, 3. diameters of all circles
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