Pythagorean theorem - math word problems - page 13 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
- Chord 4
I need to calculate the circumference of a circle, and I know the chord length c=22 cm and the distance from the center d=29 cm chord to the circle. - Trapezoid
The rectangular trapezoid ABCD with a right angle at the vertex A has sides a, b, c, and d. Calculate the circumference and the area of the trapezoid if given: a = 25cm, c = 10cm, d = 8cm - Calculate
Calculate the height to the base of the isosceles triangle ABC if the base length is c = 24cm and the arms have a length b = 13cm. - Base of an isosceles triangle
Calculate the size of the base of an isosceles triangle, the height is 5 cm, and the arm's length is 6.5 cm. What is the perimeter of this triangle?
- The ladder
The ladder has a length of 3 m and is leaning against the wall, and its inclination to the wall is 45°. How high does it reach? - Calculate 2
Calculate the largest angle of the triangle whose sides are 5.2cm, 3.6cm, and 2.1cm - RT - inscribed circle
In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at vertex C. Calculate the radius of the inscribed circle. - A square
A square with a length of diagonals 12cm gives: a) Calculate the area of a square b) rhombus with the same area as the square, has one diagonal with a length of 16 cm. Calculate the length of the other diagonal. - Rhombus
The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height
- Square inscribed
Find the length of the side of the square ABCD, which is inscribed to a circle k with a radius of 10 cm. - Garden fence
The garden has the shape of a rectangular triangle with an area of 96 square meters and a 16 m long leg. How many meters of the fence need to be fenced? - The ladder
The ladder is 10 m long. The ladder is 8 m high. How many meters is the distant heel from the wall? - Satin
Sanusha buys a piece of satin 2.4 m wide. The diagonal length of the fabric is 4m. What is the length of the piece of satin? - Isosceles trapezoid
What is the height of an isosceles trapezoid, the base of which has a length of 11 cm and 8 cm and whose legs measure 2.5 cm?
- Ladder
The ladder, 10 meters long, stays against the wall so that its bottom edge is 6 meters away from the wall. What height reaches the ladder? - Hypotenuse
Calculate the length of the hypotenuse of a right triangle if the length of one leg is 4 cm and its area is 16 square centimeters. - The ditch
Ditch with a cross-section of an isosceles trapezoid with bases 2m and 6m deep 1.5m. How long is the slope of the ditch? - Hexagon area
The center of the regular hexagon is 21 cm away from its side. Calculate the hexagon side and its area. - Triangle - is RT?
Triangle has a circumference of 90 cm. Side b is 1 cm longer than c, and side c is 31 cm longer than side a. Calculate the length of sides and determine whether a triangle is a right triangle.
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