Pythagorean theorem - math word problems - page 64 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: 1343
- 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. - Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, and √13cm. Calculate the surface and volume of the block. - Cuboidal room
The length of the cuboidal room is 2m the breadth of the cuboidal room is 3m and height is 6m find the length of the longest rod that can be fitted in the room - Sphere vs cube
How much % of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere?
- Lamp cone
Calculate the surface of a lampshade shaped like a rotary truncated cone with a base diameter of 32 cm and 12 cm and a height of 24 cm. - Hexa prism
Determine the volume of the hex prism with an edge base of 4 cm. The body height is 28 cm. - Cube - wall
V kocke ABCDEFGH je |CF|=4 √ 2. Aký je povrch kocky? - Triangular pyramid
Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm. - Prism
A right prism's length, width, and height are 17, 11, and 11, respectively. What is the length of the longest segment whose endpoints are vertices of the prism?
- Sphere cuts
At what distance from the center intersects the sphere with radius R = 91 plane if the cut area and area of the main sphere circle are in ratio 3/6? - Quadrilateral 44561
The regular quadrilateral pyramid has a volume of 212 m³ and a base edge a = 7.2 m. Calculate the surface area and height of the pyramid. - Quadrilateral 43941
Calculate the surface of a 3.5 m high quadrilateral pyramid with a rectangular base with dimensions of 3 m and 1.8 m. - Calculate 32311
Calculate the volume and surface of a cone with a base diameter of 10 dm and a side of 13 dm. - Circumference 4002
Calculate the diagonal of the cube, with the circumference of one of its walls being 48 cm. Determine its surface and its volume.
- Equilateral 2714
Determine the volume and surface of a 9 cm high triangular prism if the base is an equilateral triangle with a side of 8 cm. - A cone
A cone measures 6 inches in diameter at the base. The distance from the edge of the circumference to the top is 12 inches. Find its volume. - Surface and volume - cube
Find the surface and volume of a cube whose wall diagonal is 5 cm long. - The volume
The volume of the cone is 94.2 dm³, and the radius of the base is 6 dm. Calculate the surface of the cone. - Surface and volume
Find the surface and volume of the rotating cone if the circumference of its base is 62.8 m and the side is 25 m long.
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The Pythagorean theorem is the base for the right triangle calculator.