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: 1340
- Distance 8471
The double ladder has a height of 3 m. What height will it reach when we spread it at a distance of 1 m? - Calculate 5255
The area of the square is equal to 2.56 square meters. Calculate its diagonal. - Calculate 2673
In triangle ABC, the height on the c side is 12 cm. Calculate the area of this triangle if a = 15 cm and b = 13 cm. - Side c
In △ABC a=6, b=6 and ∠C=110°. Calculate the length of the side c. - Calculate
Calculate the height of an isosceles triangle with a base 37.8 mm long and an arm 23.1 mm long. - RT triangle and height
Calculate the remaining sides of the right triangle if we know side b = 4 cm long and height to side c h = 2.4 cm. - Spruce height
How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree? - Is right-angled
Can a triangle with the sides of sqrt 3, sqrt 5, and sqrt 8 (√3, √5, and √8) be a right triangle? - Diagonals in diamons/rhombus
Rhombus ABCD has a side length AB = 4 cm and a length of one diagonal of 6.4 cm. Calculate the length of the other diagonal. - Semicircle
To a semicircle with a diameter of 10 cm, inscribe a square. What is the length of the square sides? - Medians of isosceles triangle
The isosceles triangle has a base ABC |AB| = 16 cm and a 10 cm long arm. What is the length of the medians? - Isosceles trapezoid
Calculate the circumference and the area of the isosceles trapezoid if you know the size of the bases is 8 and 12 cm, and the size of the arms is 5 cm. - The double ladder
The double ladder has three meters-long shoulders. What is the height of the upper ladder reach if the lower ends are 1.8 meters apart? - Triangle ABC
Triangle ABC has side lengths m-1, m-2, and m-3. What has to be m to be a triangle a) rectangular b) acute-angled? - Chord 3
The chord is 2/3 of the circle's radius from the center and has a length of 10 cm. How long is the circle radius? - Logs
The log has a diameter of 30 cm. What largest beam with a rectangular cross-section can carve from it? - Without Euclid laws
Right triangle ABC with a right angle at the C has a=14 and hypotenuse c=26. Calculate the height h of this triangle without the use of Euclidean laws. - Distance two imaginary numbs
Find the distance between two complex number: z1=(-8+i) and z2=(-1+i). - Perpendicular 41811
Calculate the area of a right triangle whose longer perpendicular is six dm shorter than the hypotenuse and three dm longer than the shorter perpendicular. - Calculate 8166
Calculate the perimeter of a square when we know the length of its diagonal e = 4.2 m
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