Pythagorean theorem - math word problems - page 63 of 68
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: 1341
- 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.
- Airplane
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high does he fly? - Quadrilateral 39633
A regular quadrilateral pyramid is given: a = 27 mm, w = 21 mm (wall height). Calculate the height, volume, and surface area of the pyramid. - Calculate 82458
Calculate the volume of a cube with a wall diagonal of u = 20 cm. - Quadrilateral 82066
Calculate the volume of a regular quadrilateral pyramid with a square base of side a = 3 cm and side length b = 7 cm. - Quadrilateral 5814
Calculate the surface area and volume of a regular quadrilateral truncated pyramid if the base edges are 87 cm and 64 cm and the wall height is 49 cm.
- Centimeters 4091
Calculate the length of the body diagonal of a block whose two edges are 2 cm and 7 cm long and whose volume is equal to 49 cubic centimeters. - Dimensions 3950
Calculate the solid diagonal of a block whose dimensions are: a = 3cm, b = 5, c = 7cm. Find its volume as well. - Turning machine
What is the smallest diameter of the cylinder so that a square prism with a side of 40 cm can be turned from it? - The gable
The house's gable has the shape of an isosceles triangle, which has a base length of 14 meters, and arms with a length of 8 meters. What is the tall gable of the house? - Quadrilateral pyramid
Find the height and surface of a regular quadrilateral pyramid with a base edge a = 8cm and a wall height w = 10cm. Sketch a picture.
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