Pythagorean theorem - practice problems - page 8 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
- 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? - Billboard
A rectangular billboard is 2.5 m long with a diagonal of 2.8 m long. Calculate the perimeter and the area of the billboard. - Circumscribed circle to square
Find the length of a circle circumscribing a square side of 10 cm. Compare it to the perimeter of this square. - Is right?
Determine whether the triangle with legs (catheti) 19.5 cm and 26 cm and the length of the hypotenuse 32.5 cm is rectangular. - Triangle eq
Calculate accurate to hundredths cm height of an equilateral triangle with a side length 12 cm. Calculate also its perimeter and area. - Umbrella
Can an umbrella 75 cm long fit into a box of fruit? The box has dimensions of 390 mm and 510 mm. - Chord distance
The circle k (S, 6 cm) calculates the chord distance from the center circle S when the chord length is t = 10 cm. - RTriangle 17
The hypotenuse of a right triangle is 17 cm. If you decrease both two legs by 3 cm, you will reduce the hypotenuse by 4 cm. Determine the length of these legs. - Diagonals
The rhombus has two diagonals, e=14 dm, and f=11 dm. Calculate the side angle and height of the rhombus. - Arm
Calculate the length of the arm r of isosceles triangle ABC, with base |AB| = 14 cm and a height v=18 cm. - Diagonal
Calculate the diagonal length of the rectangle ABCD with sides a = 8 cm, b = 7 cm. - Q-Exam
If tg α = 8.6, Calculating sin α, cos α, cotg α . - Rhombus ABCD
Rhombus ABCD, |AC| = 63 cm, |BD| = 50 cm. Calculate the perimeter of the rhombus ABCD. - Proof PT
Can you easily prove Pythagoras' theorem using Euclidean theorems? If so, do it. - Diagonals of the rhombus
Calculate the height of the rhombus whose diagonals are 18 cm and 6 cm. - Equilateral triangle
Calculate the side of an equilateral triangle if its area is 886 mm². - Calculate 82490
Calculate the area of an isosceles triangle ABC with a base of 10 cm and a side of 7 cm. Sketch a picture. - Height 40911
At what height does the 15 m ladder touch the wall if its lower end is 2.5 m away from it? - Isosceles 9881
The area of an isosceles right triangle is 32 cm square. What is his circuit?
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