Pythagorean theorem - math word problems - page 66 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
Calculate the length of the wall diagonal of the cube with an edge 5 cm long. - Cube
Calculate the cube ABCDA'B'C'D's surface if the area of rectangle ACC'A' = 344 mm². - Center of the cube
The Center of the cube has a distance 16 cm from each vertex. Calculate the volume V and surface area S of the cube. - Rectangular 46201
Calculate the pyramid's surface with a rectangular base measuring 9cm and 4cm, and 6cm high.
- Calculate 46151
A pyramid has a square base with an edge length of 6 cm and a height of 6 cm. Calculate the surface of a pyramid. - Calculate 24201
Calculate the surface area, volume, and length of the body diagonal of a cube with an edge length of 4 dm. - Dimensions 4703
The block has dimensions l = 5 cm, w = 4 cm, and h = 3 cm. Calculate the length of its body diagonal. - The cone - S,V
Calculate the volume and surface area of the cone if its radius r = 6 cm and side s = 10 cm. - Pilot
How high is the airplane's pilot to see 0.001 of Earth's surface?
- Cube and sphere
A cube with a surface area of 150 cm² is described sphere. What is a sphere surface? - Wall diagonal
Calculate the length of the wall diagonal of the cube whose surface is 384 cm square. - Cone
Calculate the volume of the rotating cone with a base radius of 26.3 cm and a side 38.4 cm long. - Task
I have homework. The cube has an edge 7 cm long, and I must find the wall and body diagonal. - Vector
Calculate the length of the vector v&; 8407; = (9.75, 6.75, -6.5, -3.75, 2).
- Tetrahedron 46451
Calculate the surface of a regular tetrahedron if the length of the wall height v = 1 dm. - Find diagonal
Find the diagonal length of a cuboid with length=20m, width=25m, and height=150m. - Body diagonal
Find the length of the body diagonal of a cuboid with edges lengths of 16 cm, 7 cm, and 4 cm. - Angle of the body diagonals
Using the vector dot product calculate the angle of the body diagonals of the cube. - Three faces of a cuboid
The diagonal of the three faces of a cuboid are 13,√281, and 20 units. Then the total surface area of the cuboid is.
Do you have homework that you need help solving? Ask a question, and we will try to solve it.