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: 1340
- Isosceles 5666
In the isosceles trapezoid ABCD, calculate the missing side length "a" and its areas. Side b = d = 50 cm, c = 20 cm, height = 48 cm. - Circumference 4278
An inscribed circle is also described as an equilateral triangle with a side length of 8 cm. How many cm is the circumference of the inscribed circle smaller than the circumference of the described circle? - Calculate 2575
Calculate the area and height of the rhombic cover plate to which the following applies: d (BC) = 60 cm, angle BAD = 45 °, angle ADB = 90 °. - Calculate square 2556
Calculate the arm length b of the trapezoid ABCD if a = 12 cm, c = 4 cm, the length of AC is same as the length of BC and the area S of the triangle ABC is 9 cm square.
- Circle's 81078
The chord of a circle is 233 long, and the length of the circular arc above the chord is 235. What is the circle's radius, and what is the central angle of the circular arc? - Arithmetic mean - parabola
Find the value of k so that k² + 2k – 3 is the arithmetic mean between k² + 4k + 5 and k² – 6k + 10. - Angle of diagonals
Calculate a rectangle's perimeter and area if its diagonal is 14 cm and the diagonals form an angle of 130°. - Ladder
How long is a ladder that touches a wall 4 meters high, and its lower part is 3 meters away from the wall? - The right triangle
The right triangle ABC has a leg a = 36 cm and an area S = 540 cm². Calculate the length of the leg b and the median t2 to side b.
- Land boundary
The land is a right triangle. Its hypotenuse is 30 meters long, and its circumference is 72 meters. What are the sizes of the remaining sides of the land boundary? - KLM triangle
Find the length of the sides of the triangle KLM if m = 5cm height to m = 4.5 cm and size MKL angle is 70 degrees. - Pavement
Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if the distance of the pavement from the center is 15 m. - Decagon
Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m - Two diagonals
The diagonals of the diamond EFGH have lengths in the ratio of 1:2. What is the circumference of a rhombus if the longer diagonal is 8 cm long?
- 30-gon
At a regular 30-gon, the radius of the inscribed circle is 15cm. Find the side length a, circle radius R, circumference, and area. - Land - isosceles trapezoid
Calculate the building plot's area and perimeter in the form of an isosceles trapezoid with bases of 120m, 95m, and a height of 50m. - 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.
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