Question

34 балла)) В прямоугольном параллепипеде в основании лежит квадрат. Диагональ которого равна 3 корня из 2 см. Боковые ребра 5 см. Найти диагональ боковой грани. Срочно, ребят, пожалуйста)

Answer 1

По формуле:диагональ квадрата равна
 d=а корень из 2 ,т.е следовательно  а=d/корень из 2=3корень из 2/корень из 2=3 см.
Диагональ боковой стороны по т. Пифагора: 
D=корень из(3^2+5^2)=корень из 34 cм
Ответ: корень из 34 см.

Answer 2

Диагональ квадрата равна: d=а√2 ⇒ а=d/√2=3√2/√2=3 см.
Диагональ боковой стороны по т. Пифагора:
D=√(3²+5²)=√34 cм - это ответ.

Answer 3

Problem Analysis

We are given a rectangular parallelepiped with a square base. The diagonal of the square base is given as 3√2 cm and the length of the lateral edges is 5 cm. We need to find the diagonal of one of the lateral faces.

Solution

To solve this problem, we can use the Pythagorean theorem. Let's denote the diagonal of the square base as d and the diagonal of the lateral face as D.

According to the Pythagorean theorem, the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse. In this case, the two shorter sides are the length of the lateral edge (5 cm) and half the diagonal of the square base (d/2).

We can set up the following equation based on the Pythagorean theorem:

(d/2)^2 + (d/2)^2 = D^2

Simplifying the equation, we get:

2(d/2)^2 = D^2

d^2/2 = D^2

D = √(d^2/2)

Now, we can substitute the value of d into the equation to find D.

Calculation

Given that the diagonal of the square base is 3√2 cm, we can substitute this value into the equation:

D = √((3√2)^2/2)

Simplifying further:

D = √(9 * 2/2)

D = √9

D = 3 cm

Therefore, the diagonal of one of the lateral faces of the rectangular parallelepiped is 3 cm.

Answer

The diagonal of one of the lateral faces of the rectangular parallelepiped is 3 cm.

Please let me know if I can help you with anything else.