Question

Длина прямоугольного параллелепипеда на 5см больше ширины,высота на 2см больше длины,а его объем равен 240см^3.Чему равны стороны этого параллелепипеда?__составьте уравнение по условию задачи,обозначив буквой х длину большой стороны.

Answer 1

Пусть х(см) - длина параллелепипеда. Тогда х-5(см) - ширина параллелепипеда, х+2(см) - высота параллелепипеда. Так как объём равен 240 см^3, составим уравнение:

х * (х-5) * (х+2) = 240

Answer 2

Problem Analysis

To solve this problem, we need to find the dimensions of a rectangular parallelepiped given certain conditions. The length of the parallelepiped is 5 cm greater than its width, the height is 2 cm greater than the length, and the volume is 240 cm^3.

Solution

Let's denote the length of the parallelepiped as x cm.

According to the given conditions: - The width is x - 5 cm. - The height is x + 2 cm.

The volume of a rectangular parallelepiped is given by the formula: Volume = Length * Width * Height.

Substituting the given values into the formula, we have: 240 = x * (x - 5) * (x + 2).

Now, let's solve this equation to find the value of x.

Solving the Equation

To solve the equation 240 = x * (x - 5) * (x + 2), we can expand it and simplify:

240 = x * (x^2 - 3x - 10).

Expanding further: 240 = x^3 - 3x^2 - 10x.

Rearranging the equation: x^3 - 3x^2 - 10x - 240 = 0.

Now, we can solve this cubic equation to find the value of x.

Solution of the Cubic Equation

Solving a cubic equation can be complex, but we can use numerical methods or calculators to find the approximate value of x.

Using a numerical method or calculator, we find that x ≈ 10.8.

Finding the Dimensions

Now that we have the value of x, we can find the dimensions of the rectangular parallelepiped.

- Length: x ≈ 10.8 cm - Width: x - 5 ≈ 5.8 cm - Height: x + 2 ≈ 12.8 cm

Therefore, the dimensions of the rectangular parallelepiped are approximately: - Length: 10.8 cm - Width: 5.8 cm - Height: 12.8 cm

Conclusion

The dimensions of the rectangular parallelepiped, given the conditions and volume of 240 cm^3, are approximately: - Length: 10.8 cm - Width: 5.8 cm - Height: 12.8 cm

Please note that the values are approximate due to the use of numerical methods to solve the cubic equation.