Right triangle + quadratic equation - practice problems - page 4 of 6
Number of problems found: 110
- Find radius
Find the radius of the circle using the Pythagorean theorem where a=9, b=r, c= 6+r - Perimeter and diagonal
The perimeter of the rectangle is 82 m, and the length of its diagonal is 29 m. Find the dimensions of the rectangle. - RT and circles
Solve the right triangle if the radius of the inscribed circle is r=9 and the radius of the circumscribed circle is R=23. - Solid cuboid
A solid cuboid has a volume of 40 cm³. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.
- Sphere and cone
Within the sphere of radius G = 33 cm, inscribe the cone with the largest volume. What is that volume, and what are the dimensions of the cone? - 3d vector component
The vector u = (3.9, u3), and the length of the vector u is 12. What is, is u3? - An equilateral
An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle? - 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. - Hypotenuses 83154
In a right-angled triangle ABC with a right angle at the vertex C, the magnitudes of the hypotenuses are given ta=5, tb=2√10. Calculate the side sizes of triangle ABC and the circle's radius described by this triangle.
- Woman's day
We can easily make a heart for mothers for Woman's day by drawing two semicircles on the two upper sides of the square standing on their top. What is the radius of the circle circumscribed by this heart when the length of the side of the square is 1? - Tangents
To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle center. - A rectangle 2
A rectangle has a diagonal length of 74cm. Its side lengths are in a ratio of 5:3. Find its side lengths. - Touch x-axis
Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis. - Circle and square
An ABCD square with a side length of 100 mm is given. Calculate the circle’s radius that passes through vertices B, C, and the center of the side AD.
- Diagonals of a rhombus 2
One diagonal of a rhombus is greater than the other by 4 cm. If the area of the rhombus is 96 cm2, find the side of the rhombus. - Confectionery 7318
The confectioner needs to carve a cone-shaped decoration from a ball-shaped confectionery mass with a radius of 25 cm. Find the radius of the base of the ornament a (and the height h). He uses as much material as possible is used to make the ornament. - Rectangle 79084
A rectangle whose one side measures 35m and the other is 7m shorter than the diagonal of the rectangle. Calculate the content in m². - ABCDA'B'C'D 6261
The ABCDA'B'C'D 'prism has a square base. The wall diagonal of the AC base is 9.9 cm long, and the body diagonal AC 'is 11.4 cm long. Calculate the surface area and volume of the prism. - Parallelogram
The sides of the parallelogram are 8 cm and 6 cm long, and the diagonals' angle is 60°. What is its area?
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