Pythagorean theorem - math word problems - page 62 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: 1332
- Cube diagonals
Calculate the length of the side and the diagonals of the cube with a volume of 27 cm³. - Slant height
The cone's slant height is 5cm, and the radius of its base is 3cm, so find the cone's volume. - Cube wall
The perimeter of one cube wall is 120 meters. Calculate the surface area and the body diagonal of this cube. - Cuboid - volume, diagonals
The length of the one base edge of cuboid a is 3 cm. The body diagonal is ut=13 cm, and the diagonal of the cuboid's base is u1=5 cm. What is the volume of the cuboid? - Cut and cone
Calculate the volume of the rotation cone whose lateral surface is a circular arc with radius 15 cm and central angle 63 degrees. - Rotating cone II
Calculate the area of the surface of a rotating cone with base radius r=15 cm and height h=13 cm. - Calculate 44541
Calculate the surface and volume of the cone if you know that the base radius r = 5 dm and the side length s = 7 dm. - Measures 23791
The volume of the block is 144 cm³. The base measures 3 cm and 4 cm. How big is the body diagonal? - Hexagonal 6424
Calculate the volume and surface of a regular hexagonal prism, the base edge of which is 5 cm long and its height is 20 cm. - Right-angled triangle base
Find the volume and surface area of a triangular prism with a right-angled triangle base if the length of the prism base legs are 7.2 cm and 4.7 cm and the height of a prism is 24 cm. - The pyramid
The pyramid with a square base is 50 m high, and the sidewall height is 80 m. Find the edge of the base of the pyramid. - Height of pyramid
The pyramid ABCDV has edge lengths: AB = 4, AV = 7. What is its height? - Inscribed circle
A circle is inscribed at the bottom wall of the cube with an edge (a = 1). What is the radius of the spherical surface that contains this circle and one of the vertex of the top cube base? - A concrete pedestal
A concrete pedestal has the shape of a right circular cone and a height of 2.5 feet. The diameters of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the pedestal's lateral surface area, total surface area, and volume. - Spherical cap 4
What is the surface area of a spherical cap, the base diameter of 20 m, and the height of 2.5 m? Calculate using the formula. - Quadrangular pyramid
Given is a regular quadrangular pyramid with a square base. The body height is 30 cm, and volume V = 1000 cm³. Calculate its side and its surface area. - A box
A box is 15 centimeters long, 4 centimeters wide, and 3 centimeters tall. What is the diagonal S of the bottom side? What is the length of the body diagonal R? - Sphere equation
Obtain the equation of a sphere. Its center is on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1). - Quadrangular prism
Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal 22 cm. - Regular quadrilateral pyramid
Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm.
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