Pythagorean theorem - math word problems - page 58 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
- Calculate 83044
The cube comprises 64 small cubes, each with an edge length of 15 mm. Calculate the wall length and body diagonals. - Calculate 82700
A cone of rotation with a radius of 32 cm and side length s = 65 cm is given. Calculate the surface area and volume. - Quadrilateral 40551
Find the volume and surface area of a regular quadrilateral pyramid ABCDV if its leading edge has a length a = 10 cm and a body height h = 12 cm. - Parameters 28521
The basic parameters of the rotating cone are: Base radius 5 cm Cone height 12 cm and cone side 13 cm. Calculate: a/volume of the cone b/cone surface - Surface 19383 cone
The volume of a cone with a radius of 6 cm is 301.44 cm cubic. What is its surface? - Calculate 6214
The cube A B C D A'B'C'D 'has a section area ACC'A' equal to 64 square root of 2 cm². Calculate the surface of the cube. - Calculate 2674
Calculate the volume of the block if a = 3 cm, the size of the body diagonal is 10 cm and the size of the diagonal of the base is 5 cm - Frustrum - volume, area
Calculate the surface and volume of the truncated cone. The radius of the smaller figure is 4 cm, the height of the cone is 4 cm, and the side of the truncated cone is 5 cm. - Side edges
The regular 4-sided pyramid has a body height of 2 dm, and the opposite side edges form an angle of 70°. Calculate the surface area and volume of the pyramid. - Quadrilateral pyramid
Calculate the surface of a quadrilateral pyramid, which has a rectangular base with dimensions a = 8 cm, b = 6 cm, and height H = 10 cm. - The conical
The conical candle has a base diameter of 20 cm and a side of 30 cm. How much dm³ of wax was needed to make it? - 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? - Quadrangular pyramid
The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area. - Axial cut of a rectangle
Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long. - Cube diagonals
The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal. - Body diagonal
Cuboid with base 7cm x 3,9cm and body diagonal 9cm long. Find the height of the cuboid and the length of the diagonal of the base, - Truncated cone 5
The height of a cone is 7 cm, the length of a side is 10 cm, and the lower radius is 3cm. What could be the possible answer for the upper radius of a truncated cone? - Above Earth
To what height must a boy be raised above the earth to see one-fifth of its surface? - Hexagonal pyramid
The pyramid's base is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high. - Sphere - parts
Calculate the area of a spherical cap, which is part of an area with a base radius ρ = 10 cm and a height v = 3.4 cm.
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