Pythagorean theorem - math word problems - page 65 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
- Hexagonal pyramid
Calculate a regular hexagonal pyramid's volume and surface area with a base edge a = 30 m and a side edge b = 50 m. - Wall and body diagonals
The block/cuboid has dimensions a = 4cm, b = 3cm, and c = 12cm. Calculate the length of the wall and body diagonals. - Triangular pyramid
What is the volume of a regular triangular pyramid with a side 3 cm long? - Cone 15
The radius of the base of a right circular cone is 14 inches, and its height is 18 inches. What is the slant height?
- Body diagonal - cube
Calculate the surface and cube volume with a body diagonal 15 cm long. - Prism
Find the volume and surface area of a prism with a base of an equilateral triangle with a side of 7 dm long and a body height of 1.5 m. - Tetrahedron
Calculate the height and volume of a regular tetrahedron whose edge has a length of 13 cm. - Calculate 64654
Calculate the length of the wall and body diagonal in a cube with an edge of 60 cm. - Diagonals 7084
Calculate the lengths of the wall and body diagonals of the cube with an edge length of 10 cm.
- Consumption 4259
What is the consumption of fabric per tent: Length 250, width 180, the height of triangle 120, sides 150 (all cm). What is the volume of air in the tent? - Perpendicular 3482
The lengths of the base legs are 7.2 cm and 4.7 cm, and the height of the prism is 24 cm. Calculate the volume and surface of a triangular perpendicular prism with the base of a right triangle. - The block
The block has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this block. - Axial section
Calculate the volume and surface of a cone whose axial section is an equilateral triangle with side length a = 18cm. - The rotating
The rotating cone has a height of 0.9 m, and the diameter of the base is 7.2 dm. Calculate the surface of the cone. (Hint: use Pythagorean theorem for a side of cone)
- Pyramid height
Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm. - Equilateral tetrahedral pyramid
The base edge of a regular tetrahedral pyramid is a = 4 cm. base and walls are equilateral. Calculate the surface of this pyramid. - 4s pyramid
A regular tetrahedral pyramid has a base edge a=17 and a collateral edge length b=32. What is its height? - Calculate 40091
Calculate the size of the cube edge if the diagonal of the wall is 8 cm. - Quadrilateral pyramid
A regular quadrilateral pyramid has a volume of 24 dm³ and a base edge a = 4 dm. Calculate: a/height of the pyramid b/sidewall height c/surface of the pyramid
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