Pythagorean theorem - math word problems - page 42 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
- Vertices of a right triangle
Show that the points D(2,1), E(4,0), and F(5,7) are vertices of a right triangle. - Hyperbola
Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6]. - Right triangle - leg
Calculate the nearest tenth cm leg length in the right-angled triangle with hypotenuse length 9 cm and 7 cm long leg. - Vectors
Vector a has coordinates (8; 10), and vector b has coordinates (0; 17). If the vector c = b - a, what is the magnitude of the vector c?
- Unit vector 2D
Find coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10]. - Circle
Write the equation of a circle that passes through the point [0,6] and touches the X-axis point [5,0]: (x-x_S)²+(y-y_S)²=r² - Sprinkler 80801
A sprinkler is located in the park at a distance of 3m from the sidewalk. Water blasted up to a distance of max. 5m. What is the maximum length of the sidewalk it will cover? - Calculate 6706
Given a triangle KLM points K [-3.2] L [7, -3] M [8.5]. Calculate the side lengths and perimeter. - Calculate 4865
Calculate the length of the line segment AB, given A [8; -6] and B [4; 2]
- Quadrilateral PQRS
PQRS is a quadrilateral with P(4,4), S(8,8), and R(12,8). If vector PQ=4*vector SR, find the coordinates of Q. Solve it - Diameter
If the endpoints of the diameter of a circle are A(-9, 10) and B (-5, -4), what is the circle's radius? - Distance
Calculate the distance between two points K[6; -9] and G[5; -1]. - Vertex points
Suppose the following points of a triangle: P(-12,6), Q(4,0), R(-8,-6). Graph the triangle. Find the triangle area. - On a line
On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1].
- Triangle IRT
An isosceles right triangle ABC with right angle at vertex C has vertex coordinates: A (-1, 2); C (-5, -2). Calculate the length of segment AB. - Angle between vectors
Find the angle between the given vectors to the nearest tenth degree. u = (6, 22) and v = (10, -11) - The coordinates 2
The coordinates of the vertices of the triangle shown are A(1,7), B(5,2), and C(5,7). What is the length of segment AB in units? - A triangle 6
A triangle has vertices on a coordinate grid at H(-2,7), I(4,7), and J(4,-9). What is the length, in units, of vector HI? - Equal distance
Find the equation for all the points (x, y) that are equal in distance from points A(5,-2) and B(-2,10).
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