Question

В прямом параллелепипеде боковое ребро равно 10 см, стороны основания равны 23, 11 см, диагонали основания относятся как 2:3. Вычислить площадь диагональных сечений

Answer 1

сумма квадратов диагоналей параллелограмма = сумме квадратов всех его сторон

пусть 1 диагональ(d1)=2х, 2 диагональ(d2)=3х, тогда 4x^2+9x^2=2(529+121)

13x^2=1300

x^2=100

x1=10

x2=-10 не подходит

Параллелепипед прямой, значит боковое ребро перпендикулярно плоскости основания, H=10

d1=20, S1=d1*H=20*10=200

d2=30, S2=d2*H=30*10=300

Answer 2

Calculation of Diagonal Section Areas in a Rectangular Prism

To calculate the area of diagonal sections in a rectangular prism, we need to consider the given dimensions and ratios.

Given information: - The lateral edge of the rectangular prism is 10 cm. - The sides of the base are 23 cm and 11 cm. - The diagonals of the base are in a ratio of 2:3.

To calculate the area of the diagonal sections, we need to find the lengths of the diagonals.

Let's start by finding the lengths of the diagonals of the base.

Using the given ratio of 2:3, we can set up the following equation:

2x = length of the shorter diagonal 3x = length of the longer diagonal

Solving this equation, we find that x = 10 cm.

Therefore, the length of the shorter diagonal is 2x = 2 * 10 cm = 20 cm, and the length of the longer diagonal is 3x = 3 * 10 cm = 30 cm.

Now, we can calculate the areas of the diagonal sections.

Calculation:

To calculate the area of a diagonal section, we need to multiply the length of the diagonal by the lateral edge of the rectangular prism.

The area of the diagonal section with the shorter diagonal is:

Area = length of the shorter diagonal * lateral edge Area = 20 cm * 10 cm Area = 200 cm^2

The area of the diagonal section with the longer diagonal is:

Area = length of the longer diagonal * lateral edge Area = 30 cm * 10 cm Area = 300 cm^2

Therefore, the area of the diagonal section with the shorter diagonal is 200 cm^2, and the area of the diagonal section with the longer diagonal is 300 cm^2.

In summary: - The area of the diagonal section with the shorter diagonal is 200 cm^2. - The area of the diagonal section with the longer diagonal is 300 cm^2.

Please let me know if you need any further clarification or assistance!