Pythagorean theorem - math word problems - page 24 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: 1339
- A rectangle 2
A rectangle has a diagonal length of 74cm. Its side lengths are in a ratio of 5:3. Find its side lengths. - Rectangular garden
The sides of the rectangular garden are in a ratio of 1:2. The diagonal has a length of 20 meters. Calculate the area and perimeter of the garden. - Thunderstorm
The height of the pole before the storm is 10 m. After a storm, when they check it, they see that the ground from the pole blows part of the column. The distance from the pole is 3 meters. At how high was the pole broken? (In fact, the pole created a rect - Pendulum
Calculate the pendulum's length 2 cm lower in the lowest position than in the highest position. The circular arc length to be described when moving is 20cm. - Square
Dan's father has a square of 65.25 milligram square of wire with a diagonal. How will the square be big when one mm weighs 7 mg? - A mast
The wind broke a mast 32 meters high so that its top touches the ground 16 meters from the pole. The still standing part of the mast, the broken part, and the ground form a rectangular triangle. At what height was the mast broken? - Right trapezoid
The right trapezoid has bases 3.2 cm and 62 mm long. The shorter leg has a length of 0.25 dm. Calculate the lengths of the diagonals and the second leg. - Again saw
We have a sculpture beam from the tree trunk with a rectangular cross-section with dimensions 91 mm and 87 mm. What is the trunk's smallest diameter? - Median
In the ABC triangle is given side a=10 cm and median to side a: ta= 13 cm, and angle gamma 90°. Calculate the length of the median to side b (tb). - Road embankment
Road embankment has a cross-section shape of an isosceles trapezoid with bases 5 m and 7 m and 2 m long leg. How many cubic meters of soil is in embankment length of 1474 meters? - Chord
In a circle with a radius r=60 cm is the chord, 4× longer than its distance from the center. What is the length of the chord? - Right-angled 81989
Using Euclid's Theorems and Pythagoras' Theorem, complete the following parameters describing a right-angled triangle ABC with a right angle at vertex C if we know b=10, cb=8 - Crossbars 80697
Calculate the length of the middle crossbars in an isosceles triangle if the length of the arm is 52mm and the base height is 48mm - Difference 80618
A regular hexagon is described and inscribed in a circle. The difference between its areas is 8√3. Find the circle's radius. - Fifteen-spruce 57291
A mighty gale broke the top of the fifteen-spruce spruce, resting it on the ground. The distance of this top from the trunk was 4.6 m below. At what height was the spruce trunk broken? - Calculate 47763
Calculate the area of an isosceles trapezoid ABCD, whose longer base measures 48 cm, the shorter base measures 3/4 of the longest base, and the leg of the trapezoid measures 2/3 of the longer base. The result is rounded to the nearest hundredth. - Isosceles 27793
The LICH isosceles trapezoid has 5.2 cm long arms and its bases are 7.6 cm and 3.6 cm long. Find the area of the LICH trapezoid. - Triangle 8027
Side a in the right triangle has size a = 120 mm, angle A = 60°. How big is the hypotenuse c? - Circumference 7823
The bases are 9 cm and 5 cm long in a rectangular trapezoid. The length of the shorter arm is 3 cm. Calculate its circumference and area. - Isosceles 5575
The picture shows an isosceles triangle VLK with a center of gravity of T. The base VL measures 16 cm, and the line KK1 measures 18 cm. How long is the VV1 line?
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