Pythagorean theorem - practice problems - page 6 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 aspect ratio
The aspect ratio of the rectangular triangle is 13:12:5. Calculate the internal angles of the triangle. - Is right triangle or not
If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area. - Diagonals of diamond
Find the area and circumference of the diamond ABCD with 15m and 11m diagonals. - Two diagonals
The rhombus has a side length of 12 cm and a length of one diagonal of 21 cm. What is the length of the second diagonal? - Diagonal of the rectangle
Calculate the rectangle's diagonal, which area is 54 centimeters square, and the circuit is equal to 30 cm. - Windbreak
A tree at the height of 3 meters broke in the windbreak. Its peak fell 4.5 m from the tree. How tall was the tree? - Rectangle
The rectangle is 18 cm long and 10 cm wide. Determine the diameter of the circle circumscribed to the rectangle. - Diamond
The side length of the diamond is 35 cm, and the length of the diagonal is 56 cm. Calculate the height and length of the second diagonal. - RT 10
The area of the right triangle is 84 cm², and one of its catheti is a=10 cm. Calculate the perimeter of the triangle ABC. - Isosceles III
The base of the isosceles triangle is 17 cm area 416 cm². Calculate the perimeter of this triangle. - Circumference 72414
Calculate the diagonal and the area of a square if its circumference is 10 centimeters. - Perimeter 6254
Perimeter and area of the rectangle. Diagonal 260m and one side 150m - Isosceles triangle
Find the area of an isosceles triangle whose leg is twice the base, b=1 - Right triangle
A right triangle ABC is given, and c is a hypotenuse. Find the length of the sides a, b, the angle beta if c = 5 and angle alfa = A = 35 degrees. - Integer sides
A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side? - Diamond area from diagonals
In the diamond, ABCD is AB = 4 dm, and the diagonal length is 6.4 dm long. What is the area of the diamond? - Five-gon
Calculate the side a, the circumference, and the area of the regular 5-angle if Rop = 6cm. - Tree trunk
What is the smallest diameter of a tree trunk that we can cut a square-section square with a side length of 20 cm? - The perimeter
The perimeter of equilateral △PQR is 12. The perimeter of the regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to STUVWX? - Double ladder
The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
Do you have homework that you need help solving? Ask a question, and we will try to solve it.