System of equations + triangle - practice problems - page 4 of 8
Number of problems found: 151
- Three parallels
The vertices of an equilateral triangle lie on three different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle. - Sides of right angled triangle
One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle. - Faces diagonals
If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), find the cuboid volume. Solve for x=1.3, y=1, z=1.2 - Two chords
Calculate the length of chord AB and perpendicular chord BC to the circle if AB is 4 cm from the circle's center and BC 8 cm from the center.
- Circumference 9811
Kristýna chose a certain odd natural number divisible by three. Jakub and David then examined triangles with a circumference in millimeters equal to the number selected by Kristýna and whose sides have lengths in millimeters expressed by different integer - Calculate 9701
In the triangle, the side length AB = 6 cm, the height per side c = 5 cm, and the angle BCA = 35°. Calculate sides a b. - Touch x-axis
Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis. - The second
The second angle of a triangle is the same size as the first angle. The third angle is 12 degrees larger than the first angle. How large are the angles? - Triangle 42
Triangle BCA. Angles A=119° B=(3y+14) C=4y. What is the measure of triangle BCA=?
- Parallelogram
The sides of the parallelogram are 8 cm and 6 cm long, and the diagonals' angle is 60°. What is its area? - Isosceles triangle
In an isosceles triangle, the arm's length and the length of the base are in a ratio of 3 to 5. What is the length of the arm? - Rectangular triangle
The lengths of the rectangular triangle sides with a longer leg of 12 cm form an arithmetic sequence. What is the area of the triangle? - Angle at the apex
In an isosceles triangle, the angle at the apex is 30° greater than the angle at the base. How big are the internal angles? - Circumference 7655
The triangle has a circumference of 35 cm. One side is four times longer than the other and, at the same time, 1 cm longer than the third. Determine the sides of the triangle.
- Circumference 7615
The sides of the rectangle are in a ratio of 3:5. Its circumference is 48 cm. Calculate the length of its diagonal. - Quadrilateral 7583
For the sizes of the interior angles of the quadrilateral ABCD, the following applies: the angle alpha is 26° greater than the angle beta, twice the angle Beta is 5° less than the angle gamma, and the angle gamma is 36° greater than the angle delta. Deter - AP RT triangle
The length of the sides of a right triangle forms an arithmetic progression, and the longer leg is 24 cm long. What are the perimeter and area? - Calculate 6885
Triangle with o = 16.8 cm and aspect ratio a:c = 1:2 and b:c = 5:6. Calculate side lengths a =? B =? c =? - Sphere from tree points
Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
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