Pythagorean theorem - math word problems - page 59 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
- Horizon
The top of a lighthouse is 19 m above the sea. How far away is an object just "on the horizon"? [Assume the Earth is a sphere of radius 6378.1 km.] - Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16? - Measures 3162
What is the surface of a regular pyramid with a square base? If each edge of the base measures 40 mm, the pyramid's height is 44 mm, and the pyramid's height is 38 mm. - Measures 2535
Peter wants to hide a 60 cm long whistle in a shoebox that measures 25 cm x 48 cm x 21 cm. Will he make it? - Inscribed 81949
A cube is inscribed in a sphere with a radius of 27 cm. Calculate its volume and surface area. - Calculate 73434
Calculate the volume and surface area of the cone with a diameter of 20 cm and a height of 15 cm. - Calculate 66254
Calculate the volume and surface of a regular hexagonal prism with a height v = 2cm and a base edge a = 8cm. - Substantial 65114
Calculate the volume of a regular triangular prism with a substantial edge length of 8 cm and a prism height of 17 cm. - Perpendiculars 36213
A right triangle with perpendiculars a = 3 cm and b = 4 cm rotates around a longer perpendicular. Calculate the volume and surface area of the resulting cone. - Quadrilateral 13881
Please calculate the volume of a quadrilateral pyramid when a = 5cm and the wall height is w = 12cm. - Quadrilateral 8220
Calculate the volume of a regular quadrilateral pyramid, whose wall height is w = 12 cm and the edge of the base is a = 5 cm. - Hexagonal 8200
The tops of the base of a regular hexagonal pyramid lie on a circle with a radius of 10 cm. The height of the pyramid is 12cm. What is its volume? - Calculate 2558
Calculate the size of the solid diagonals of a prism with a rhombus base if the sizes of the base diagonals are 16 cm and 20 cm and the height of the prism is 32 cm. Calculate the size of the base edge. - Slant height 2
A regular triangular pyramid with a slant height of 9 m has a volume of 50 m³. Find the lateral area of the pyramid. - Surface area and volume
Find the surface area and volume of a rotating cone whose diameter is 60 mm and side length 3.4 cm. - Calculate
Calculate the cone's surface and volume from the rotation of the right triangle ABC with the squares 6 cm and 9 cm long around the shorter squeegee. - Wall height
Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height w = 20 cm. - The quadrilateral pyramid
The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area. - Hexagon
Calculate the regular hexagonal prism's surface whose base edge a = 12cm and side edge b = 3 dm. - Pyramid four sides
A regular tetrahedral pyramid has a body height of 38 cm and a wall height of 42 cm. Calculate the surface area of the pyramid; the result is round to square centimeters.
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