Pythagorean theorem - math word problems - page 20 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
- Circle annulus
There are two concentric circles in the figure. The chord of the larger circle, 10 cm long, is tangent to the smaller circle. What does annulus have? - Sum of squares
The sum of squares above the sides of the rectangular triangle is 900 cm². Calculate the area of the square over the triangle's hypotenuse. - Chord
It is given to a circle k(r=6 cm), and the points A and B such that |AB| = 8 cm lie on k. Calculate the distance of the center of circle S to the midpoint C of segment AB. - Right triangle eq2
The hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.
- The field
The player crossed the field diagonally and walked the length of 250 m. Calculate the length of the field circumference if one side of the field is 25 meters. - Circle chord
Calculate the length of the chord of the circle with radius r = 10 cm, the length of which is equal to the distance from the circle's center. - The cellar
Mr. Novák has a cellar, and a cellar window in the chalet has a 0.6-meter square window. The window wishes to place an X-shaped grid in a square. He uses iron welded bars. Calculate the lengths of individual bars and the total length of the bars he has to - Right triangles
How many right triangles we can construct from line segments 3,4,5,6,8,10,12,13,15,17 cm long? (Do not forget the triangle inequality). - RT leg and perimeter
The right triangle ABC with hypotenuse c has the length of a leg a= 84 and the perimeter of the triangle o = 269. Calculate the size of the sides of the triangle ABC.
- Rectangle and circle
The rectangle ABCD has side lengths a = 40 mm and b = 30 mm and is circumscribed by a circle k. Calculate approximately how many centimeters a circle is long. - Chord 2
Point A has a distance of 13 cm from the circle's center with a radius r = 5 cm. Calculate the length of the chord connecting the points T1 and T2 of contact of tangents led from point A to the circle. - Area 4gon
Calculate the area of 4-gon, two, and the two sides are equal and parallel with lengths 11, 5, 11, and 5. Inner angles are 45°, 135°,45°, 135°. - Sea
How far can you see from the ship's mast, whose peak is at 14 meters above sea level? (Earth's radius is 6370 km). - Parallelogram 82626
Calculate the area of a parallelogram if we know the perimeter is 23 cm, the diagonal is 8.5 cm, and one side is 1.5 cm longer.
- Quadrilateral 78874
Given is a quadrilateral ABCD inscribed in a circle, with the diagonal AC being the circle's diameter. The distance between point B and the diameter is 15 cm, and between point D and the diameter is 18 cm. Calculate the radius of the circle and the perime - Perpendicular 40203
In a right triangle, one perpendicular is 5 cm longer than the other perpendicular. The diaphragm is 150 mm. Calculate the lengths of the hangings. - Calculate 8252
Calculate in cm² the area of a circle whose diameter is equal to the length of the diagonal of a square ABCD with a side of 4cm. - Against 6754
A ladder leans against the wall. It touches the wall at the height of 240cm. Its lower end is 100 cm distant from the wall. How long is the ladder? - Carpenter 4227
The carpenter leaned the two-meter kitchen counter against the wall. The lower edge is 0.75m away from the wall. At what height from the ground is the board's top edge resting?
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