The distance from some point to the plane of the rectangle is equal to the root

| July 18, 2021 | education

The distance from some point to the plane of the rectangle is equal to the root of 5 cm, and to each of its vertices is 3 cm. Find the diagonal of the rectangle.

If the distance from a point in space to the vertices of the polygon (in particular, a rectangle) is the same, then this point will be projected to the center of the circumscribed circle. In the rectangle ABCD, this is the intersection point of the diagonals O. And the distance from the point to the plane is the length of the perpendicular MO, dropped from the point to plane, the base of which will be in the center of the rectangle. By the condition MO = 3 cm, and MA = √5 cm. From the right-angled triangle AMO, by the Pythagorean theorem, we have OA = √9 – 5 = √4 = 2. OA is half of the diagonal of the rectangle. The entire AC diagonal = 4.

Answer: the required diagonal AC = 4.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.