Pythagorean theorem - math word problems - page 60 of 67
The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as:c2 = a2 + b2
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
A common proof of the Pythagorean Theorem is called the "area proof". To prove the theorem using this method, we can create a square with side length c and two smaller squares with side lengths a and b, as shown in the figure. We can then place the smaller squares next to each other to form a rectangle with area a x b. We can then see that the area of the square with side length c is equal to the sum of the areas of the smaller squares, which is equal to the area of the rectangle. This demonstrates that c2 = a2 + b2, as stated in the theorem.
Another proof is Euclidean proof which is based on the Euclidean geometry and construction of a line segment that is c and perpendicular to the line segment of a and b.
Number of problems found: 1340
- Rotating cone
Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm. - 3s prism
It is given a regular perpendicular triangular prism with a height of 19.0 cm and a base edge of 7.1 cm. Calculate the volume of the prism. - 3sides prism
The base of a vertical prism is an isosceles triangle whose base is 10 cm, and the arm is 13 cm long. Prism height is three times the height of the base triangle. Calculate the surface area of the prism. - Pyramid
Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC.
- Axial section
The axial section of the cylinder has a diagonal 40 cm. The shell size and base surface are in the ratio 3:2. Calculate the volume and surface area of this cylinder. - Pyramid a+h
Calculate the pyramid's volume and surface area with the edge and height a = 26 cm. h = 3 dm. - Logs
The trunk diameter is 52 cm. Is it possible to inscribe a square prism with a side 27 cm? - Calculate 81560
The cone's surface is 75.36 cm, and the radius is 3 cm. Calculate the volume of the cone. - Equilateral 73374
The axial section of the cone is an equilateral triangle with a side of 12 cm. Surface and volume calculation.
- Dimensions 48161
A block with dimensions a = 15cm b = 5cm and a block height c = 8cm. Calculate the length of the wall diagonal in the base. - Cone-shaped 47363
We built a cone-shaped shelter with a base diameter of 4 m on the children's playground. Calculate the cone shell if the side of the cone measures 8 m - Calculate 26991
How can you calculate the wall height of a pyramid when you know: the length of the base edge: is 28 mm and: the body height: is 42 mm? - Centimeters 5533
Calculate the area of one cube wall and the wall diagonal of a cube if its volume equals 1728 cubic centimeters. - Square-shaped 4821
The vertical prism lies on a square-shaped base with a side 3 cm long. The diagonal of the sidewall of the prism is u = 5cm. Calculate the volume of this prism.
- Perpendicular 3146
The base of the vertical prism is a right triangle with a perpendicular 5 cm. The area of the largest wall is 130 cm2, and the body's height is 10 cm. Calculate the surface area of the body. - Cone - side
Find the cone's surface area and volume if its height is 125 mm and the side length is 17 cm. - Hexagonal pyramid
Find the volume of a regular hexagonal pyramid, the base edge 12 cm long and the side edge 20 cm. - Spherical cap
The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut. - Height of the cuboid
Cuboid with a rectangular base, measuring 3 cm and 4 cm diagonal, has a body 13 centimeters long. What is the height of the cuboid?
Do you have homework that you need help solving? Ask a question, and we will try to solve it.