Pythagorean theorem - practice problems - page 9 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: 1332
- Equilateral 5571
The height in the equilateral triangle ABC measures the square root of 3 cm. What is the length of the center bar of this triangle? - Calculate 5499
Calculate the area of the circle, which is described by a square with a side length of 7.5 cm. - Hypotenuse 3554
Calculate the hypotenuse length if you know the area of an isosceles right triangle that is 24.5 cm square. - Calculate 2420
The kite is tied to a string 85 meters long and hovers over a place 60 meters away from us. Calculate how high the dragon hovers. - Calculate 2201
Calculate the diagonals in the deltoid with sides of 10, 12.6, and 5 cm. - Circumference 1608
The bases of the isosceles trapezoid measure 110m and 50m. The distance between the bases is 40m. Calculate its circumference. - Estate
An estate-shaped rectangular trapezoid has bases long 35 m, 65 m, and perpendicular arm 34 m. Calculate how long its fence is. - ET inscribed circle
An equilateral triangle has been inscribed in a circle with a radius of 4 cm . Find the area of the shaded region. - Base and longest side
The base of a right-angled triangle is 10 centimeters, and the longest side is 26 centimeters. What is the area of the triangle? - Side and diagonal
Find the circumference and the area of the rectangle if given: side a = 8 cm diagonal u = 10 cm. - Is right triangle
Find out if the triangle ABC (with right angle at the vertex C) is right if: a) a = 3dm, b = 40cm, c = 0.5m b) a = 8dm, b = 1.2m, c = 6dm - The trapezium
The trapezium is formed by cutting the top of the right-angled isosceles triangle. The trapezium base is 10 cm, and the top is 5 cm. Find the area of the trapezium. - Diamond and diagonals
A diamond has diagonals f = 8 cm and g = 6 cm long. How long is this diamond perimeter? (Calculate it!) - Isosceles triangle
Calculate the area and perimeter of an isosceles triangle ABC with base AB if a = 6 cm, c = 7 cm. - Square s3
Calculate the diagonal of the square, where its area is 0.49 cm square. And also calculate its circumference. - Rhombus OWES
OWES is a rhombus, given that OW is 6cm and one diagonal measures 8cm. Find its area? - Ladder
The ladder has a length of 3.5 meters. It is leaning against the wall, so the bottom end is 2 meters from the wall. Find the height of the ladder. - Park
In the park is a marked diamond-shaped line connecting locations A, D, S, C, B, and A. Calculate its length if |AB| = 108 m, |AC| = 172.8 m. - Drainage channel
The cross-section of the drainage channel is an isosceles trapezoid whose bases have a length of 1.80 m and 0.90 m, and the arm has a length of 0.60 meters. Calculate the depth of the channel. - Concentric circles
In the circle with diameter, 13 cm is constructed chord 1 cm long. Calculate the radius of a concentric circle that touches this chord.
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