Question

Диагональ параллелепипеда равна 13, а стороны основания 3 и 4. Найти длину высоты, найти диагональную площадь сечения.

Answer 1

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Answer 2

Calculation of Height Length:

To find the length of the height of the parallelepiped, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right 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.

In this case, the diagonal of the parallelepiped is given as 13, and the lengths of the base sides are given as 3 and 4. Let's denote the length of the height as h.

Using the Pythagorean theorem, we can set up the following equation:

h^2 = 13^2 - 3^2 - 4^2

Simplifying the equation:

h^2 = 169 - 9 - 16

h^2 = 144

Taking the square root of both sides:

h = √144

h = 12

Therefore, the length of the height of the parallelepiped is 12.

Calculation of Diagonal Section Area:

To find the diagonal section area of the parallelepiped, we need to find the area of the cross-section formed by the diagonal. The cross-section is a rectangle with sides equal to the lengths of the base sides.

The area of a rectangle is given by the formula: Area = length × width.

In this case, the lengths of the base sides are given as 3 and 4. Let's denote the diagonal section area as A.

Using the formula for the area of a rectangle, we can calculate the diagonal section area as:

A = 3 × 4

A = 12

Therefore, the diagonal section area of the parallelepiped is 12.

Please let me know if there's anything else I can help you with!