Question

Никто не может решить?-------------------------------------------------------------------------в прямоугольном параллелепипеде ABCDA1B1C1D1 известно, что BB1=16, A1B1=2, A1D1=8. Найдите длину диагонали AC1.-------------------------------------------------------------------------

Answer 1

рассмотрим треугольник A1D1C1 (провели диагональ A1C1). он прямоугольнй.

найдем А1С1 по т. Пиф. : х в квадрате = 64+4. х= 2 корня из 17.

 

рассмотрим треугольник  AA1C1. АА1 перпендикулярно А1С1, А1С1 - проекция АС1 .

найдем АС1 по т.П.

у в квадрате = 68 + 256 = 324.

у = 18

 

Ответ: АС1 = 18

Answer 2

Поскольку параллепипед прямоугольный, то можно применить

а^2+б^2=с^2

известны все стороны, которые примыкают к прямым углам

1) опреляем длину диагонали АС

АД=А1Д1=ВС=В1С1

АВ=А1В1=ДС=Д1С1

АА1=ВВ1=СС1=ДД1

АС=корень(АВ^2+ВС^2) = корень(2^2+8^2)=корень(68)

2) определяем длину диагонали АС1

АС1=корень(АС^2+СС1^2) = корень([68]^2+16^2) = корень(324) = 18

Answer 3

Problem Statement

В прямоугольном параллелепипеде ABCDA1B1C1D1 известно, что BB1=16, A1B1=2, A1D1=8. Найдите длину диагонали AC1.

Solution

To find the length of the diagonal AC1 in the rectangular parallelepiped ABCDA1B1C1D1, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In this case, we can consider the diagonal AC1 as the hypotenuse of a right triangle, with AB1 and A1C1 as the other two sides. Let's denote the length of AC1 as x.

According to the Pythagorean theorem, we have the following equation:

AB1^2 + A1C1^2 = AC1^2

We are given that BB1 = 16, A1B1 = 2, and A1D1 = 8. To find the lengths of AB1 and A1C1, we can use the properties of a rectangular parallelepiped.

In a rectangular parallelepiped, opposite sides are equal in length. Therefore, AB1 = A1D1 = 8.

Substituting the values into the equation, we have:

8^2 + A1C1^2 = x^2

Simplifying the equation, we get:

64 + A1C1^2 = x^2

To find the value of A1C1, we can use the given value of A1B1.

We are given that A1B1 = 2. Since opposite sides of a rectangular parallelepiped are equal, A1C1 = A1B1 = 2.

Substituting the value of A1C1 into the equation, we have:

64 + 2^2 = x^2

Simplifying further, we get:

68 = x^2

Taking the square root of both sides, we find:

x = √68

Therefore, the length of the diagonal AC1 is √68.

Answer

The length of the diagonal AC1 in the rectangular parallelepiped ABCDA1B1C1D1 is √68.