Pythagorean theorem - math word problems - page 11 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
- The diamond
The diamond has 35 cm-wide sides, and the diagonals are in a ratio of 1:2. Calculate the diagonal lengths. - Perimeter of triangle
In the triangle, ABC angle A is 60°, angle B is 90°, and side size c is 15 cm. Calculate the triangle circumference. - Rectangle
The rectangle has a perimeter of 75 cm. The diagonal length is 32.5 cm. Determine the length of the sides. - Circular ring
A square with an area of 16 centimeters is inscribed circle k1 and described to circle k2. Calculate the area of the circular ring, which circles k1, and k2 form. - Rhombus 2
Calculate the rhombus area with a height v=48 mm and shorter diagonal u = 60 mm long. - Right angled triangle
The hypotenuse of a right triangle is 17 cm long. When we decrease the length of the legs by 3 cm, then decrease its hypotenuse by 4 cm. Find the size of its legs. - Triangle
Calculate the triangle sides if its area S = 630 and the second cathetus is shorter by 17. - Leg
Determine the trapezoid area with bases 32 and 12; the height is 2 shorter than its leg. - Chord - TS v2
The radius of circle k measures 72 cm. Chord GH = 11 cm. What is TS? - EQL triangle
Calculate the inradius and circumradius of an equilateral triangle with side a=77 cm. - Oil rig
The oil drilling rig is 23 meters in height and fixes the ropes, which ends are 10 meters away from the foot of the tower. How long are these ropes? - Circle chord
What is the length x of the chord circle of diameter 115 m if the distance from the center circle is 11 m? - Arithmetic 80808
The lengths of the sides of a right triangle form the first 3 terms of the arithmetic sequence. The content is 6cm². - Calculate 69104
The diagonal of the TV screen is 82 cm, and the height is 40 cm. Calculate the width of the screen. - Triangle's 63774
Calculate the perimeter of an isosceles triangle if the triangle's height is 15 cm and the base is 16 cm. - Calculate 60423
In a right triangle RST with a right angle at the vertex T, we know the lengths of two sides: s = 7.8 cm and t = 13 cm; calculate the third party r. - Calculate 6149
Find the area and perimeter of a square whose diagonal is 10 cm. - Millimeters 6019
In an isosceles right triangle, the arms' length is 50 mm, and the height at the base is 35.35 mm. Calculate the perimeter of this triangle in millimeters. - Diagonal 5555
The pool has a diamond shape with a side 20m long. One diagonal is 32 meters. What is the second diagonal? - Determine 4258
Determine the length of the side of the diamond, with its two diagonals being 12 cm and 6 cm long.
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