Length - high school - practice problems - page 2 of 31
Number of problems found: 616
- Semicircle 82687
If the shell of a cone is a semicircle, then the diameter of the cone's base is equal to its side's length. Prove it. - A raft
I want to build a raft, and I have beams with a square section with side a=20cm and length l=2m, wood density 670 kg/m³. I will connect 10 beams - what is the volume of the raft and its weight? How deep will a raft sink in water (water density 1000kg/m³)? - Circle - analytics geometry
Write the equation of the circle that passes through the points Q[3.5] R[2.6] and has its center on the line 2x+3y-4=0. - Calculated 82619
When modifying the school plot in the shape of a rectangle, the deviation was calculated if we increased the length and width of the plot by 1m and its area by 22 m². If we reduce the length of the plot by 2m and increase its width by 1m, its area will de
- Calculate 82578
The vertices of triangle ABC are: A[1, 2, -3], B[0, 1, 2], C[2, 1, 1]. Calculate the lengths of sides AB, AC and the angle at vertex A. - Double-return 82524
Calculate at what distance from the axis of rotation a force of 60N acts on one side of a double-return lever; if a force of 180N acts on the other side at a distance of 1 meter from the axis of rotation, the lever is in equilibrium. - Determine 82478
Determine the equation of the parabola that has the point F = [3,2] as its focus and the line x+y+1=0 as its shift line. - Hypotenuse 82370
A line segment AA1 of length 6 cm is given. Construct all triangles ABC for which AA1 is the hypotenuse, side length BC is 5 cm, and angle gamma is 60°. - Determine 82341
Determine the equation of the circle that is the set of all points of the plane that are twice as far from the point [3,7] as they are from the point [0,1].
- Calculate 82144
Calculate the height of side b (v_b) of triangle ABC with vertices A[4;1;3] B[2;3;3] and C[1;1;3]. - Closest 82051
On the line p: 2x + y + 1 = 0, find the point A ∈ p that is closest to the point P =(1,0) - Equilateral 81142
The rotating body was created by rotating an equilateral triangle with a side length of a=2 cm around one of its sides. Calculate the volume of this rotating body. - 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. - Right-angled 81126
In a right-angled triangle, the hypotenuse has a length of 24 cm. The heel of the height on the hypotenuse divides it into two parts in a ratio of 2:4. What size in cm is the height at the hypotenuse? Calculate the perimeter of this right triangle in cent
- Circle's 81078
The chord of a circle is 233 long, and the length of the circular arc above the chord is 235. What is the circle's radius, and what is the central angle of the circular arc? - Cross-sectional 80979
An undisciplined motorcyclist drove at an unreasonable speed on a mountain road, lost control in a bend, and left the roadway at 90 km/h. He was falling into a gully 36 m deep. Draw a cross-sectional picture of the whole situation. How far did the motorcy - Elevation 80869
We can see the top of the tower standing on a plane from a certain point A at an elevation angle of 39° 25''. If we come towards its foot 50m closer to place B, we can see the top of the tower from it at an elevation angle of 56° 42''. How tall is the tow - Elevation 80866
Find the height of the tower when the geodetic measured two angles of elevation α=34° 30'' and β=41°. The distance between places AB is 14 meters. - Centimeters 80859
Triangle ABC and triangle ADE are similar. Calculate in square centimeters the area of triangle ABC if the length of side DE is 12 cm, the length of side BC is 16 cm, and the area of triangle ADE is 27 cm².
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