Pythagorean theorem - math word problems - page 14 of 68
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: 1342
- Cableway
The cableway has a length of 1800 m. The horizontal distance between the upper and lower cable car station is 1600 m. Calculate how much meters altitude is higher upper station than at the base station. - RT and ratio
A right triangle whose legs are in a ratio 6:12 has a hypotenuse 68 m long. How long are its legs? - ISO Triangle V2
The perimeter of the isosceles triangle is 474 m, and the base is 48 m longer than the arms. Calculate the area of this triangle. - Triangle and its heights
Calculate the length of the sides of the triangle ABC if va=5 cm, vb=7 cm and side b are 5 cm shorter than side a.
- Square 2
Points D[10,-8] and B[4,5] are opposed vertices of the square ABCD. Calculate the area of the square ABCD. - Calculation 81402
In an isosceles triangle, the side a=b= 21 cm, and the triangle's height is 19 cm. Find out the base and perimeter of the triangle (sketch, calculation, answer). - String 63794
The chord AB is in the circle k with a radius of 13 cm. The center C of the string AB is 5 cm from the center S of the circle. How long is the AB string? - Calculate 39131
A circle describes a square with a side of 8 cm. Calculate the area of the rest of the circle if we cut out the square. - Rectangle 8017
Calculate the other side of the rectangle if one side and the length of the diagonal are known: a = 3cm u = 5cm b =?
- Circumference 7615
The sides of the rectangle are in a ratio of 3:5. Its circumference is 48 cm. Calculate the length of its diagonal. - Circumference 4003
Calculate the diagonal length of a rectangle whose length is 3 cm greater than its width and whose circumference is 18 centimeters. - Calculate 3987
The diamond has an area of 94.24 square meters and one diagonal of 7.6 cm. Calculate the length of the second diagonal. - Equilateral 2543
a) The perimeter of the equilateral triangle ABC is 63 cm. Calculate the side sizes of the triangle and its height. b) A right isosceles triangle has an area of 40.5 square meters. How big is his circuit? c) Calculate the square's area if the diagonal's s - 11990 perimeter RT
A right triangle has integer side lengths and a perimeter of 11990. In addition, we know that one of its perpendiculars has a prime number length. Find its length.
- Arm and base
The isosceles triangle has a circumference of 46 cm. If the arm is 5 cm longer than the base, calculate its area. - Rhombus and diagonals
The lengths of the diamond diagonals are e = 48cm f = 20cm. Calculate the length of its sides. - Isosceles triangle
Calculate the size of the interior angles and the length of the base of the isosceles triangle if the arm's length is 17 cm and the height of the base is 12 cm. - Company logo
The company logo consists of a blue circle with a radius of 4 cm and an inscribed white square. What is the area of the blue part of the logo? - Three altitudes
A triangle with altitudes 4, 5, and 6 cm is given. Calculate the lengths of all medians and all sides in a triangle.
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