Pythagorean theorem - practice problems - page 6 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
- Square and circles
Square with sides 83 cm is circumscribed and inscribed with circles. Determine the radiuses of both circles. - Ladder 35331
The ladder is 13 m long, and its lower part is 5 m away from the wall. How high does the ladder reach? - Distance 7717
To what height does a 6.5 m long ladder leaning against a wall at a distance of 5.4 m reach? - Circumscribed 7290
Calculate the area of a regular hexagon if the radius of the circle circumscribed is 6.8 cm.
- Diagonally 2838
The square plot has an area of 324m². Calculate the length of the road that runs diagonally across the plot. - Two parallel chords
The two parallel chords of the circle have the same length of 6 cm and are 8 cm apart. Calculate the radius of the circle. - Isosceles trapezium
Calculate the area of an isosceles trapezium ABCD if a = 10cm, b = 5cm, c = 4cm. - Diagonal to area
Calculate the area of a rectangle in which the diagonal length is 10 cm. - Square circles
Calculate the length of the described and inscribed circle to the square ABCD with a side of 5cm.
- Chord 5
It is given a circle k / S; 5 cm /. Its chord MN is 3 cm away from the center of the circle. Calculate its length. - Acreage
What acreage has a rectangular plot whose diagonal is 34 meters long, and one side has a length of 16 meters? ... - Trapezoid ABCD
Calculate the perimeter of trapezoid ABCD if we know the side c=12, b=19, which is also a height, and side d=32. - Rhombus
Calculate the length of the diagonal AC of the rhombus ABCD if its perimeter is 84 dm and the other diagonal BD has length 20 dm. - Height UT
How long is the height in the equilateral triangle with a side e = 15?
- Rectangle SS
The perimeter of a rectangle is 268 cm, and its diagonal is 99.3 cm. Determine the dimensions of the rectangle. - Square diagonal
Calculate the length of the square diagonal if the perimeter is 172 cm. - Calculate 80636
Calculate the distance of a chord 19 cm long from the center of a circle with a diameter of 28 cm. - Calculation 18413
What is the length of the cathetus of an isosceles right triangle with an 8 cm long hypotenuse? Make calculations and procedures. - Calculate 4228
A circle k (S, 5cm) is given. Calculate the length of the chord of the circle k if it is 3 cm from the center S.
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