Basic functions + reason - practice problems - page 52 of 99
Number of problems found: 1976
- Triangle 3187
In a general triangle, the aspect ratio a: b = 2:3. What is the ratio of heights va: vb? - Mysterious area
The trapezoid ABCD is given. Calculate its area if the area of the DBC triangle is 27 cm². - Squares 5479
Draw two stone squares. They have a total of 34 stones. What edges do the squares have? - 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? - Calculate 14733
Square has the side a = 12 cm. Calculate the area of a triangle in the square. - Rhombus 29
One of the diagonals of a rhombus is equal to a side of the rhombus. Find the angles of the rhombus. - Isosceles from square
How many isosceles triangles form in a square when we mark all diagonals? - Is right triangle
Decide if the triangle XYZ is rectangular: x = 4 m, y = 6 m, z = 4 m
- N-gon angles
What is the sum of interior angles 8-gon? What is the internal angle of a regular convex 8-polygon? - Hypotenuse 82331
Given a right triangle KLM with a right angle at M. What is the magnitude of the hypotenuse m if the magnitude of the normal to the hypotenuse m is 4? - Identical 20963
In which triangles is the line identical with the height? - Quatrefoil 81138
Gothic quatrefoil is an ornament in which four identical touching smaller circles are inscribed in a larger circle, as you can see in the picture. The radius of the great circle is one meter. Calculate the radius of the smaller circle in meters. - Circumference 6382
Jan bought a large rectangle plot with a circumference of 90 meters. He divided it into three rectangular plots. The shorter side has all three plots of the same length. Their longer sides are three consecutive natural numbers. Find out each plot's dimens
- Flowerbed
We enlarged the circular flower bed, so its radius increased by 3 m. The substrate consumption per enlarged flower bed was (at the same layer height as before magnification) nine times greater than before. Determine the original flowerbed radius. - Square into three rectangles
Divide the square with a side length of 12 cm into three rectangles with the same circumference so that these circumferences are as small as possible. - 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? - Carpet
The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make a rectangular cut of a roll. That piece of carpet will be the longest possible and will fit into the room. How long is a piece of carpet? Note: The carpet will not be parallel w - Trapezoid thirds
The ABCD trapezoid has parallel sides AB and CD. The E point lies on the AB side. The segment DE divides the trapezoid into two parts with the same area. Find the length of the AE line segment.
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