Pythagorean theorem - practice problems - page 5 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
- Broken tree
The tree is broken at 4 meters above the ground. The top of the tree touches the ground at a distance of 5 meters from the trunk. Calculate the original height of the tree. - Diagonal - simple
Calculate the length of the diagonal of a rectangle with dimensions 5 cm and 12 cm. - Equilateral triangle v2
An equilateral triangle has a perimeter 36 dm. What is its area? - Goniometric form
Determine the goniometric form of a complex number z = √ 110 +4 i. - Base
Compute the base of an isosceles triangle, with the arm a=20 cm and a height above the base h=10 cm. - Circumference 56291
Calculate the circumference of a circle circumscribed by a right triangle with squares 10 cm and 15 cm long. - Perpendiculars 46081
Calculate the size of the hypotenuse in a triangle if its perpendiculars are 8 cm and 8.4 cm long. - Calculate 7762
Calculate the size of the diagonal of an ABCD square whose perimeter is 40cm - Calculate 6198
Calculate the diagonal length of the 87 cm and 60 cm TVs and round the result to units. - Greatest angle
Calculate the greatest triangle angle with sides 124, 323, 302. - The diagonals
The diagonals in the diamond ABCD are 6 cm and 8 cm long. What is the perimeter of this diamond? - The triangle
The triangle has sides 5 cm long, 5 cm, and 8 cm long. What is the area of the triangle? - ABC isosceles
ABC isosceles rights triangle the length of each leg is 1 unit what is the length of the hypotenuse AB in the exact form - Right isosceles triangle
What can be the area of a right isosceles triangle with a side length of 8 cm? - Hypotenuse
Calculate the length of the hypotenuse of a right triangle with a catheti 71 cm and 49 cm long. - Moivre 2
Find the cube roots of 125(cos 288° + i sin 288°). - Euclid 5
Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm. - Inscribed rectangle
The circle area is 216. Determine the area of the inscribed rectangle with one side 5 long. - Rhombus
Find the length of the other diagonal and the area of the rhombus. The perimeter of a rhombus is 40 cm, and one of the diagonals is of length 10 cm. - Rhombus
Calculate the perimeter and area of a rhombus whose diagonals are 39 cm and 51 cm long.
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