Question

АВСД квадрат со стороной равна корень из 2см.О точка пересечения диагоналей,ОЕ перпендикуляр к плоскости АВС,ОЕ равно корень из 3см. найдите расстояние от точки Е до вершин квадрата ​

Answer 1

Ответ:

2см

Объяснение:

АС=AD*√2=√2*√2=2 см

АО=АС/2=2/2=1 см.

∆АЕО- прямоугольный треугольник

По теореме Пифагора

АЕ=√(ЕО²+АО²)=√((√3)²+1²)=√(3+1)=√4=2см

Answer 2

Given Information:

We are given that the side length of square ABCD is equal to the square root of 2 cm. The point of intersection of the diagonals is E, and EO is perpendicular to the plane of ABCD, with EO equal to the square root of 3 cm.

Solution:

To find the distance from point E to the vertices of the square, we can use the Pythagorean theorem. Since the square is regular, all sides are equal in length.

Let's assume that the side length of the square is s cm.

Using the Pythagorean theorem, we can find the distance from point E to the vertices of the square:

1. Distance from E to A: - We can form a right triangle with sides EA, EO, and OA. - The length of EO is given as the square root of 3 cm. - The length of OA is half the length of the diagonal of the square, which is s * sqrt(2). - Using the Pythagorean theorem, we have: ``` EA^2 = EO^2 + OA^2 EA^2 = (sqrt(3))^2 + (s * sqrt(2))^2 EA^2 = 3 + 2s^2 EA = sqrt(3 + 2s^2) cm ```

2. Distance from E to B: - We can form a right triangle with sides EB, EO, and OB. - The length of EO is given as the square root of 3 cm. - The length of OB is half the length of the diagonal of the square, which is s * sqrt(2). - Using the Pythagorean theorem, we have: ``` EB^2 = EO^2 + OB^2 EB^2 = (sqrt(3))^2 + (s * sqrt(2))^2 EB^2 = 3 + 2s^2 EB = sqrt(3 + 2s^2) cm ```

3. Distance from E to C: - We can form a right triangle with sides EC, EO, and OC. - The length of EO is given as the square root of 3 cm. - The length of OC is half the length of the diagonal of the square, which is s * sqrt(2). - Using the Pythagorean theorem, we have: ``` EC^2 = EO^2 + OC^2 EC^2 = (sqrt(3))^2 + (s * sqrt(2))^2 EC^2 = 3 + 2s^2 EC = sqrt(3 + 2s^2) cm ```

4. Distance from E to D: - We can form a right triangle with sides ED, EO, and OD. - The length of EO is given as the square root of 3 cm. - The length of OD is half the length of the diagonal of the square, which is s * sqrt(2). - Using the Pythagorean theorem, we have: ``` ED^2 = EO^2 + OD^2 ED^2 = (sqrt(3))^2 + (s * sqrt(2))^2 ED^2 = 3 + 2s^2 ED = sqrt(3 + 2s^2) cm ```

Therefore, the distance from point E to each vertex of the square is sqrt(3 + 2s^2) cm.

Please note that we need the value of s (the side length of the square) to calculate the exact distances. The given information does not provide the value of s, so we cannot calculate the exact distances without that information.