Pythagorean theorem - math word problems - page 40 of 68
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: 1342
- Equilateral 35073
Draw an equilateral triangle ABC with a side of 8.5 cm. Assemble all the mines and measure them. What is the difference between the longest and the shortest of them? - Lengths of medians from coordinates
There is a triangle ABC: A [-6.6; 1.2], B [3.4; -5.6], C [2.8; 4.2]. Calculate the lengths of its medians. - Construct 80719
Construct a rectangle ABCD if a = 8cm and the length of the diagonal AC is 13cm. Measure the length of the sides of the rectangle. - Triangle 67504
Sestroj triangle HOP, if o = 6 cm, h = 8 cm and | PHO | = 90 °
- Three parallels
The vertices of an equilateral triangle lie on three different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle. - Circle described
The circle radius described in the right triangle with a 6 cm long leg is 5 cm. Calculate the circumference of this triangle. - Displacement 55871
Assemble the two offsets, d1, and d2, shown by OA and OB oriented lines. The coordinates of the points are O = (0m, 0m), A = (3m, 3m), and B = (5m, 2m). Measure the magnitude of the resulting displacement d. - Calculate 16223
The following elements are known in the right triangle ABC: a = 10 cm, height to side c h = 9.23 cm. Calculate o, R (radius of the inscribed circle), r (radius of the inscribed circle). - Touch circle
Point A has a distance (A, k) = 10 cm from a circle k with radius r = 4 cm and center S. Calculate: a) the distance of point A from the point of contact T if the tangent to the circle is drawn from point A b) the distance of the contact point T from the l
- Three points
Three points K (-3; 2), L (-1; 4), M (3, -4) are given. Find out: (a) whether the triangle KLM is right b) calculate the length of the line to the k side c) write the coordinates of the vector LM d) write the directional form of the KM side e) write the d - Sides of right angled triangle
One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle. - Tangent
What distance are the tangent t of the circle (S, 4 cm) and the chord of this circle, which is 6 cm long and parallel to the tangent t? - Right angled triangle 2
LMN is a right-angled triangle with vertices at L(1,3), M(3,5), and N(6,n). Given angle LMN is 90° find n - Length of the chord
Calculate the length of the chord in a circle with a radius of 25 cm with a central angle of 26°.
- Three
Three points are given: A (-3, 1), B (2, -4), C (3, 3) a) Find the perimeter of triangle ABC. b) Decide what type of triangle the triangle ABC is. c) Find the length of the inscribed circle - On line
On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0]. - Center of line segment
Calculate the distance of point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t; t is from interval <0,1>. - Calculate 82144
Calculate the height of side b (v_b) of triangle ABC with vertices A[4;1;3] B[2;3;3] and C[1;1;3]. - Calculate 66814
Calculate the area and perimeter of the right triangle ABC if A [5.5; -2.5] B [-3; 5] C [-3; -2.5]
Do you have homework that you need help solving? Ask a question, and we will try to solve it.