Planimetrics + reason - practice problems
Number of problems found: 212
- Hairs
Suppose the length of the hair is affected by only the α-keratin synthesis, which is the major component. This synthesis takes place in the epithelial cells of the hair bulb. The structure of α-keratin is made up of α-helix for the 3.6 amino acid residues - Strawberries 82738
Three classmates worked part-time during the summer vacation harvesting strawberries. Jan collected 145 baskets of strawberries during the entire time of the brigade. Peter collected 185 baskets. How many baskets did their classmate Stan collect, if we kn - Circumference 7143
Peter drew a regular hexagon, the vertices of which lay on a circle 16 cm long. Then, for each vertex of this hexagon, he drew a circle centered on that vertex that ran through its two adjacent vertices. The unit was created as in the picture. Find the ci - Triangles
Hanka cut the 20 cm long straws into three pieces. Each piece had a length in cm. Then, with these three pieces, she tried to make a triangle. a) What circuit has each of the triangles? b) How long can the longest side measure? c) How many different trian - Quadrangular 4559
The quadrangular garden should be fenced off with a slatted fence. The sides of the orchard are 65m, 78m, 40m and 32m. The wheels are to be placed 6m apart, and the axes of the rims are 15cm apart. How much is needed for a wheel fence, and how many batten - Tablecloth 72254
The table top is 1.2 m long, 55 cm wide, and 35 mm thick. Calculate how many regular meters of a 1 m wide roll are needed for a tablecloth that extends 15 cm beyond the bottom edge of the table on all sides. - Horizontally 5480
Let's have a 4x6 grid, i.e., with 5x7 grid points. Can each grid point be colored white or blue so that each point has an even number of white neighbors? At the same time, those points that are connected by one line of the grid are considered to be neighb - Clocks
What distance will describe the tip of a minute hand 6 cm long for 20 minutes when we know the starting position with finally enclosed hands each other 120°? - Tiles path
A rectangular park measures 24mX18m. A path 2.4m wide is constructed all around it. Find the cost of paving the path with cement tiles of size 60cm X 40cm at the rate of $5.60 per tile. - Non-woven 7322
A square sandpit should have a side length of 1.6 m. How long do you need a wooden board to enclose the sandpit? Under the sandbox, a non-woven fabric will extend by 0.2 m on each side. How much will we need? - trapezium 3428
Given is a trapezoid ABCD with bases AB, CD. Let K be side AB's midpoint, and point L be side CD's midpoint. The area of triangle ALB is 15 cm2, and the area of triangle DKC is 10 cm². Calculate the area of trapezium ABCD. - Washer
The washing machine drum washes at 71 RPM. The washing machine motor pulley has a diameter of 8 cm. What must be the diameter of the drum machine pulley when the motor is at 351 RPM? - Equator
Suppose that a tourist went on foot over the Globe equator. How many meters more track made his hat on his head as the shoes on your feet? The radius of the Earth is $R km, and the height of the tourist is $v m. - The plot
Mr. Duma recently inherited a rectangular plot, part of the estate left by his late father. The plot with the following dimensions: Length=2x+1; Width=x-1. Determine the formula, in terms of x, that best describes the area of the rectangular plot. He has - Chickens and rabbits
In the yard were chickens and rabbits. Together they had 23 heads and 76 legs. How many chickens and how many rabbits were in the yard? - Rectangles
How many different rectangles with sides integers (in mm) have a circumference of exactly 1000 cm? (a rectangle with sides of 50cm and 450cm is considered to be the same as a rectangle with sides of 450cm and 50cm) - Irregular pentagon
A rectangle-shaped, 16 x 4 cm strip of paper is folded lengthwise so that the lower right corner is applied to the upper left corner. What area does the pentagon have? - Annulus
Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n. - Tablecloth
The table top is 90 cm long and 50 cm wide. How many cm of lace edging is necessary for the tablecloth that hangs on each side by 10 cm? - Right triangles
How many right triangles we can construct from line segments 3,4,5,6,8,10,12,13,15,17 cm long? (Do not forget the triangle inequality).
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