Pythagorean theorem - math word problems - page 19 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
- 30-meter 45481
The 30-meter tree broke. Its top fell 5m from the trunk. At what level did it break? - Calculate 35911
Calculate the height of the house's roof, which has the shape of an isosceles triangle with a base of 8.4 m and arms of 6.5 m. - Perpendicular 32733
Calculate the right triangle ABC, the perpendicular b = 43.5 cm of the hypotenuse c = 72.9 cm. Calculate: A hypotenuse segment cb, side a, a hypotenuse segment ca, and a height of triangle v - Rectangular 26091
The circular running track has a diameter of 130 meters. Can a rectangular surface with dimensions of 12m and 50m be grassed inside the circle? - Circumscribed 22713
Calculate the circumference and the area of a regular ten-angle polygon if the radius of the circumscribed circle r = 20 cm. - Surrounded 13601
The letter H is part of a square surrounded by a circle with a diameter of 42 cm. Is a fabric 1 meter long enough to make this letter? Neglect the thickness of the fabric. - Circumference 7052
The trapezoid ABCD is given (AB || CD, AB perpendicular to AD). Calculate its circumference if | AB | = 20cm, | CD | = 15cm, | AD | = 12cm. Pythagorean theorem - Calculate: 6679
In the right triangle ABC, we know the right angle γ, the area S = 48 cm2, and the side a = 8 cm. Calculate: pages b, c - Circumference 4430
In an isosceles triangle with a circumference of 36 cm, the height at the base is 12 cm long. Calculate the length of the arm of a given triangle. - Circumference 4421
The area of an equilateral triangle is 81 times three below the square root of cm². Calculate its circumference. - Circle's chords
The circle has two chord lengths, 30 and 34 cm. The shorter one is from the center twice as a longer chord. Determine the radius of the circle. - Stairway
The stairway has 20 steps. Each step has a length of 22 cm and a height of 15 cm. Calculate the length of the handrail of staircases if the top and bottom exceed 10 cm. - Rectangle
Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees. - Determine 79864
Determine by how many meters the deviated tower, whose height is 56m, and the top of the tower is located at 55.855m. - Sides ratio and angles
In triangle ABC, you know the ratio of side lengths a:b:c=3:4:6. Calculate the angle sizes of triangle ABC. - Ratio of triangles areas
In an equilateral triangle ABC, the point T is its center of gravity, the point R is the image of the point T in axial symmetry along the line AB, and the point N is the image of the point T in axial symmetry along the line BC. Find the ratio of the areas - The storm
After the storm, the top of the 5 m high mast deviated by 1 m from the original vertical axis. What is the peak now? Round to 2 decimal places. - An equilateral
An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle? - Rectangular trapezoid
In a rectangular trapezoid ABCD with right angles at vertices A and D with sides a = 12cm, b = 13cm, c = 7cm. Find the angles beta and gamma and height v. - Cable car
Find the elevation difference of the cable car when it rises by 67 per mille, and the rope length is 930 m.
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