Question

Покажите что длина диагонали d прямого параллелепипеда с измерениями a, b, и c (длина, ширина, высота) определяются по формуле d^2=a^2+b^2+c^2

Answer 1

На твой вопрос простой ответ 18

Answer 2

Calculation of the Diagonal Length of a Rectangular Prism

The formula to calculate the diagonal length (d) of a rectangular prism with dimensions a, b, and c (length, width, and height) is given by:

d^2 = a^2 + b^2 + c^2 Let's break down the formula and explain each component:

- d: Diagonal length of the rectangular prism. - a: Length of the rectangular prism. - b: Width of the rectangular prism. - c: Height of the rectangular prism.

By substituting the values of a, b, and c into the formula, we can calculate the diagonal length (d) of the rectangular prism.

Please note that the formula assumes that the rectangular prism is a right rectangular prism, meaning that all angles between the sides are right angles.

Let's move on to an example to illustrate the calculation.

Example Calculation

Suppose we have a rectangular prism with the following dimensions: - Length (a) = 3 units - Width (b) = 4 units - Height (c) = 5 units

To calculate the diagonal length (d), we can substitute these values into the formula:

d^2 = a^2 + b^2 + c^2

d^2 = 3^2 + 4^2 + 5^2

d^2 = 9 + 16 + 25

d^2 = 50

Taking the square root of both sides, we find:

d = √50

d ≈ 7.07 units

Therefore, the diagonal length (d) of the rectangular prism with dimensions a = 3 units, b = 4 units, and c = 5 units is approximately 7.07 units.

Conclusion

In conclusion, the diagonal length (d) of a rectangular prism with dimensions a, b, and c can be calculated using the formula d^2 = a^2 + b^2 + c^2. By substituting the values of a, b, and c into the formula, we can determine the diagonal length of the rectangular prism.