Planimetry - math word problems - page 105 of 187
Number of problems found: 3739
- Coordinates
Determine the coordinates of the vertices and the area of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0, and the diagonal on the line 3x + 2y + 3 = 0 - Right triangle from axes
A line segment has its ends on the coordinate axes and forms a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment? - Ruler
Peter is looking at John over a ruler that keeps at an arm's distance of 60 cm from the eye, and on the ruler, John measured the height of 15 mm. John is 2 meters high. How far from Peter stands John? - Angles
In the triangle ABC, the ratio of angles is α:β = 4:5. The angle γ is 36°. How big are the angles α and β? - Lunes of Hippocrates
Calculate the sum of the area of the so-called Hippocratic lunas, which were cut above the legs of a right triangle (a = 6 cm, b = 8 cm). Instructions: First, calculate the area of the semicircles above all sides of the ABC triangle. Compare the sum of th - Circles
In the circle with a radius, 7.5 cm is constructed of two parallel chords whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions, write both). - Table paper coverage
The table has the shape of a rectangle with dimensions of 80 × 100 cm. Ten identical sheets of paper measuring 20 x 30 cm lie next to each other on it. Papers do not overlap or extend beyond the surface of the table. What part of the table surface is cove - Circular dragon
The dragon has the shape of a circular section with a central angle of 40° and a radius of 35 cm. How much paper do we need to make if 10% is added to the curved ones? - Triangles
Hannah cut 20 cm straws into three pieces. Each piece had an integer length in centimetres. She then tried to form a triangle from the three pieces. a) What is the perimeter of each such triangle? b) What is the maximum possible length of the longest side - Clock triangle angles
On the circular face of the clock, we connect the points corresponding to the numbers 2, 9, and 11, which creates a triangle. Calculate the sizes of all the interior angles of that triangle. - Hexagon in circle
Calculate the radius of a circle whose length is 10 cm greater than the circumference of a regular hexagon inscribed in this circle. - Square Area Parallel Lines
What is the area of a square when the distance between parallel lines is 6? - Triangle ABC
There is the triangle ABC with the side BC of length 2 cm. Point K is the middle point of AB. Points L and M split the AC side into three equal lines. KLM is an isosceles triangle with a right angle at point K. Determine the lengths of the sides AB, AC tr - Mr. Filip
Mr. Philip is preparing to renovate a garden. He will divide its area into herb, vegetable, and ornamental sections in the ratio 2:3:5 (in this order). The area of the herb section will be 4 m × 2.5 m. a) Calculate the total area of the renovated garden i - Express
Express the equation of the function: a/prices of cucumbers for the number of cucumbers sold, if one cucumber costs CZK 5 b/the area of the rectangle on side b, if side a measures 5 cm c/the perimeter of the rectangle on side b, if side a measures 5 cm d/ - Two chords
Two parallel chords are drawn in a circle with a radius r = 26 cm. One chord has a length of t1 = 48 cm, and the second has a length of t2 = 20 cm, with the center lying between them. Calculate the distance between two chords. - Medians in triangle
The median of the isosceles triangle is 3 cm long. If its perimeter is 16 cm, determine the size of its sides. - Circle
The circle touches two parallel lines, p, and q, and its center lies on line a, which is the secant of lines p and q. Write the equation of the circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0 - Rectangle Dimensions Reduce Ratio
Reduce the dimensions of the rectangle with dimensions of 21 cm and 3 dm in a ratio of 4:6. In what proportion will the areas of both rectangles be? - Mice
Mice consumed a circular hole in a slice of cheese. The cheese is a circular cut with a radius of 20 cm and an angle of 90 degrees. What percentage of the cheese ate mice if they made 20 holes with a diameter of 2 cm?
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