Pythagorean theorem - math word problems - page 16 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
- Regular n-gon
Which regular polygon has a radius of circumscribed circle r = 10 cm and the radius of inscribed circle p = 9.962 cm? - Diagonals
Given a rhombus ABCD with a diagonal length of 8 cm and 12 cm. Calculate the side length and area of the rhombus. - RT perimeter
The leg of the rectangular triangle is 7 cm shorter than the second leg and 8 cm shorter than the hypotenuse. Calculate the triangle circumference. - Rectangular trapezium
Calculate the perimeter of a rectangular trapezium when its area is 576 cm² and side a (base) is 30 cm, height 24 cm. - Forces
Determine the resultant of two perpendicular forces F1 = 560 N and the second force 25% smaller. - Chord AB
What is the chord AB's length if its distance from the center S of the circle k(S, 92 cm) is 10 cm? - Rectangular trapezoid
Calculate the area of a rectangular trapezoid with a right angle at point A and if |AC| = 4 cm, |BC| = 3 cm, and the diagonal AC is perpendicular to the side BC. - Column
The vertical pole high $v m tall broke, and its toe fell $x m from the bottom of the pole. At what height above the ground does the pole break? - The circle arc
Calculate the span of the arc, which is part of a circle with diameter d = 11 m and its height is 5 m. - Square
Rectangular square has side lengths 183 and 244 meters. How many meters will measure the path that leads straight diagonally from one corner to the other? - Octagon
We have a square with a side 56 cm. We cut corners to make his octagon. What will be the side of the octagon? - Equilateral 80573
The field has the shape of an equilateral triangle. Calculate its content if you know that the side is 280 meters long. - Calculate 79144
The circle's radius is r=8.9 cm, and the chord AB of this circle has a length of 16 cm. Calculate the distance of chord AB from the center of the circle. - Circumference 46171
Calculate the circumference and area of a rectangle with one side 6 cm long and a diagonal 10 cm long. - Calculate 27441
Calculate the length of the side of the square if the size of the diagonal u = 9.9 cm is entered. - Isosceles 19393
How many dm² of the area is an isosceles triangle if the angle at the base is 45˚ and the bottom is 10 cm long? - Must-have 7893
If we want to make a prism with a wooden base with a 5 cm side of a wooden bar, what is the bar's smallest diameter? - Calculate: 6686
We know the right angle γ, side b = 14 cm, and height vc = 8.8 cm in the right triangle ABC. Calculate: angle α = angle β = side a = side c = - Rectangular 4624
The lengths of the sides of the rectangular garden are in the ratio of 1:2. The junction of the centers of adjacent sides is 20 m long. Calculate the perimeter and acreage of the land. - Calculated: 2839
A trapezoid is given: c = 4.2 cm, h = 8 cm, S = 42.4 cm, d = 8.4 It would help if you calculated the following: sides a and b, and perimeter o:
Do you have homework that you need help solving? Ask a question, and we will try to solve it.