Pythagorean theorem - practice problems - page 2 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
- Annular area
The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area. - Find radius
Find the radius of the circle using the Pythagorean theorem where a=9, b=r, c= 6+r - Square
Calculate the square's perimeter and area with a diagonal length of 30 cm. - Diagonal of square
Calculate the side of a square when its diagonal is 10 cm. - Diamond side
The diagonals of the diamond are 18 cm and 14 cm long. Calculate the length of the diamond side. - Circles
The area of a circle inscribed in a square is 14. What is the area of a circle circumscribed around a square? - Circle chord
Determine the circle's radius in which the chord 6 cm away from the center is 12 cm longer than the circle's radius. - Leg and height
Solve right triangle with height v = 9.6 m and shorter cathetus b = 17.3 m. - Equilateral 37341
Calculate an equilateral triangle's perimeter and area with a side of 20 dm. - Perpendicular 5516
In a right triangle, one perpendicular is 1 m shorter than the hypotenuse. The other perpendicular is 2 m shorter than the hypotenuse. Find the lengths of all sides of the triangle. - Iso triangle
An isosceles triangle with a base of 8 cm. Its circumference is 28 cm. Calculate the height of the triangle. - Tv screen
The length of its diagonal gives the size of a tv screen. If the dimension of a tv screen is 16 inches by 14 inches, what is the TV screen size? - Perimeter of circle
Calculate the circumference of a described circle to the triangle with sides 9,12,15 cm. - Length IT
Find the length (circumference) of an isosceles trapezoid in which the length of the bases a,c, and the height h is given: a = 8 cm c = 2 cm h = 4 cm. - Diamond
Calculate the length of the two diagonals of the diamond if: a = 13 cm v = 12 cm - Median
In the right triangle are sides a=96 dm b=31 dm. Calculate the length of the medians tc to the hypotenuse. - Calculate 35411
The given is an isosceles triangle with a base of 24dm and an arm of 15dm. Calculate the height of the triangle. - Circumference 3919
Determine the diagonal of a square whose circumference is equal to 72 cm. - Calculate 3373
Calculate the PT sling if the length of one sling is 1.2 dm and the diaphragm length is 1.3 dm. - Diagonal 2738
ABCD square has a diagonal length of 8 cm. What is the area of the square?
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