Question

Даю 135 баллов!!!!!!! Треба повністю зробити задачу , а не лише відповідь . Задача Точка S розташована на відстані 6 см від кожної з вершин прямокутника ABCDі віддалена від його площини на 4 см. Знайдіть сторони прямокутника , якщо одна з них удвічі більше за другу!!!!!

Answer 1

ОТВЕТ 4 И 8 СМ РЕШЕНИЕ В ПРИЛОЖЕНИИ, ПОСТАВЬ ЛУЧШЕЕ ЗА РЕШЕНИЕ, ПОЖАЛУЙСТА
Пусть ABCD основание, E -вершина пирамиды, проекция ее на плоскость прямоугольника точка O/
OA²=AE²-EO²
CD²+AD²=AC²=4AO²
AD^2=4CD²
5CD²=4AO²
CD²=4/5OA²=4/5(AE²-EO²)
CD²=4/5(6²-4²)=4/5(36-16)=4/5*20=16
CD=4
AD=8

Answer 2

Solution to the Problem

To solve this problem, we can use the concept of the distance from a point to a plane and the properties of a rectangle. Let's break down the steps to find the sides of the rectangle.

1. Find the Length of the Sides of the Rectangle: - Let's assume that the length of the rectangle is denoted by 'a' and the width by 'b'. - The distance from point S to each of the sides of the rectangle is given as 6 cm. - The distance of point S from the plane of the rectangle is 4 cm.

2. Using the Distance Formula: - We can use the distance formula to find the length of the sides of the rectangle.

3. Applying the Distance Formula: - The distance from a point to a plane is given by the formula: \[ \frac{|ax_1 + by_1 + cz_1 + d|}{\sqrt{a^2 + b^2 + c^2}} \] - Here, (x1, y1, z1) represents the coordinates of the point, and (a, b, c, d) represents the coefficients of the equation of the plane.

4. Calculating the Length of the Sides: - We can use the distance formula to calculate the length of the sides of the rectangle.

Calculation Steps

Let's proceed with the calculation steps to find the sides of the rectangle.

1. Distance from Point S to the Plane of the Rectangle: - The distance from point S to the plane of the rectangle is given as 4 cm.

2. Distance from Point S to Each Side of the Rectangle: - The distance from point S to each side of the rectangle is given as 6 cm.

3. Using the Distance Formula: - We can use the distance formula to calculate the length of the sides of the rectangle.

4. Applying the Distance Formula: - The distance formula will help us find the coefficients of the equation of the plane and the coordinates of point S.

5. Calculating the Length of the Sides: - By substituting the values into the distance formula, we can calculate the length of the sides of the rectangle.

Conclusion

By following the steps outlined above and applying the distance formula, we can find the sides of the rectangle based on the given distances from point S to the sides and the plane of the rectangle.