Equation + Pythagorean theorem - practice problems - page 4 of 10
Number of problems found: 185
- 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? - Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, and √13cm. Calculate the surface and volume of the block. - Three faces of a cuboid
The diagonal of the three faces of a cuboid are 13,√281, and 20 units. Then the total surface area of the cuboid is. - Suppose
Suppose you know that the length of a line segment is 15, x2=6, y2=14, and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not?
- Parametric form
Calculate the distance of point A [2,1] from the line p: X = -1 + 3 t Y = 5-4 t Line p has a parametric form of the line equation. - 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. - Land boundary
The land is a right triangle. Its hypotenuse is 30 meters long, and its circumference is 72 meters. What are the sizes of the remaining sides of the land boundary? - 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. - 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.
- The hemisphere
The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees? - Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base of 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure. - Medians in right triangle
It is given a right triangle, and angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. How to calculate the length of the sides? - 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.
- Touch x-axis
Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis. - Three altitudes
A triangle with altitudes 4, 5, and 6 cm is given. Calculate the lengths of all medians and all sides in a triangle. - Isosceles triangle 9
There is an isosceles triangle ABC where AB= AC. The perimeter is 64cm, and the altitude is 24cm. Find the area of the isosceles triangle. - Ratio of sides
Calculate the area of a circle with the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in a ratio of 2 to 7. - RT sides
Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
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