Pythagorean theorem - math word problems - page 15 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
- Isosceles triangle
The leg of the isosceles triangle is 5 dm, and its height is 20 cm longer than the base. Calculate base length z. - Isosceles
Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area. - Angles by cosine law
Calculate the size of the angles of the triangle ABC if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem). - Chord circle
The circle to the (S, r = 8 cm) are different points A, B connected segment /AB/ = 12 cm. AB mark the middle of S'. Calculate |SS'|. Make the sketch.
- Rhombus IV
Calculate the length of the diagonals of the rhombus, whose sizes are in the ratio of 1:2 and a rhombus side is 35 cm. - Rectangle - desc circle
The length of the sides of the rectangle is at a ratio of 1:3. The circle's radius circumscribed to the rectangle is 10 cm. Calculate the rectangle's perimeter. - RT 11
Calculate the area of the right triangle if its perimeter is p = 45 m and one cathetus is 20 m long. - Ladder
8.3 meters long ladder is leaning against the wall of the well, and its lower end is 1.2 meters from this wall. How high from the bottom of a well is the top edge of the ladder? - Right isosceles
Calculate the area of the isosceles right triangle whose perimeter is 26 cm.
- Square diagonal
Calculate the length of the diagonal of the square with side a = 11 cm. - Common chord
Two circles with radii 18 cm and 20 cm intersect at two points. Its common chord is long 11 cm. What is the distance of the centers of these circles? - Height 2
Calculate the height of the equilateral triangle with side 48. - Against 82851
A 3.4 m long ladder is leaning against a wall. Its lower end is 1.6 m away from the wall. At what height does the ladder touch the wall? - Determine 82595
A ladder is 7 meters long and is leaning against a wall so that its lower end is 4 meters away from the wall. Determine how high the ladder reaches
- Circumference 82552
The isosceles trapezoid has a base length of 12 cm, a height of 4.5 cm, and a height of 5 cm. What is its circumference? - Calculate 20643
Calculate the area and perimeter of the building plot in the shape of an isosceles trapezoid with a base of 120 m, 95 m, and a height of 50 m. - Perimeter 7882
The diagonals of the diamond are 2.4 dm and 1.8 dm long. What is the perimeter of this diamond? - Perpendicular 7712
Calculate the length of the shadow of a ladder 8 m long leaning against a 6 m high wall. (the sun shines perpendicular to the ladder - see picture). - Height—the 6183
In the isosceles trapezoid ABCD, the base length is a = 10cm, c = 6cm, and the arm's length is 4cm. Calculate its height—the result round to tenths.
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