Pythagorean theorem - practice problems - page 4 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
- 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? - Calculate 2577
Calculate the length of the circle chord, which is 2.5 cm from the circle's center. The radius is 6.5 cm. - Calculate 2566
Calculate the area of a regular hexagon with side a = 2cm
- Area of a rectangle
Calculate a rectangle area with a diagonal of u = 12.5cm and a width of b = 3.5cm. Use the Pythagorean theorem. - The chord
Calculate a chord length where the distance from the circle's center (S, 6 cm) equals 3 cm. - OPT
What is the perimeter of a right triangle with the legs 14 cm and 21 cm long? - Rhombus
The rhombus with area 137 has one diagonal that is longer by 5 than the second one. Calculate the length of the diagonals and rhombus sides. - Square2
The side of the square is a = 5.6 cm. How long is its diagonal?
- Circle
The circle k with diameter |MN| = 61. Point J lies on the circle k. Line |MJ|=22. Calculate the length of a segment JN. - Surrounded 36661
Calculate the length of the circle, which is surrounded by a square with a side length of 3 cm - Calculate 10691
Calculate the length of the side of a square whose diagonal has a length of 10 m. - Supported 6172
The ladder is 1.4 m from the wall and touches 3 m high. How long is the ladder? - Embankment 2539
The profile of the railway embankment has the shape of an isosceles trapezoid, where a = 16.4 m, c = 10.6 m, and b = d = 5.2 m. Calculate the embankment height.
- Trio 2
Decide whether a trio of numbers is the side of a right triangle: 26,24,10. - Euklid4
The legs of a right triangle have dimensions 244 m and 246 m. Calculate the length of the hypotenuse and the height of this right triangle. - Is right?
Is a triangle with sides 51, 56, and 77 right triangle? - Tangent of an angle
Suppose the tangent of an angle of a right-angled triangle is 0.8. Then its longest side is: - Equilateral triangle
Calculate the area of an equilateral triangle with a circumference of 72cm.
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