Question

Высота прямоугольного параллелепипеда равна 13 см. Ширина на 5 см меньше длины. Найдите наименьшую из сторон основания, если объем параллелепипеда равен 1092см3. ОТВЕТ:7 см. Просьба написать решение...

Answer 1

наименьшая из сторон основания у меня тоже вышла 7 см

Answer 2

Problem Analysis

We are given the height of a rectangular parallelepiped (13 cm) and the width is 5 cm less than the length. The volume of the parallelepiped is given as 1092 cm^3. We need to find the smallest side length of the base.

Solution

Let's assume the length of the parallelepiped is x cm. According to the problem, the width is 5 cm less than the length, so the width would be (x - 5) cm. The height is given as 13 cm.

The volume of a rectangular parallelepiped is calculated by multiplying the length, width, and height. So we can set up the following equation:

Volume = Length * Width * Height

1092 = x * (x - 5) * 13

Simplifying the equation:

1092 = 13x^2 - 65x

Rearranging the equation to form a quadratic equation:

13x^2 - 65x - 1092 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 13, b = -65, and c = -1092. Plugging in these values into the quadratic formula:

x = (-(-65) ± √((-65)^2 - 4 * 13 * (-1092))) / (2 * 13)

Simplifying further:

x = (65 ± √(4225 + 56784)) / 26

x = (65 ± √(61009)) / 26

x = (65 ± 247) / 26

We have two possible solutions for x:

1. x = (65 + 247) / 26 = 312 / 26 = 12 2. x = (65 - 247) / 26 = -182 / 26 = -7

Since the length cannot be negative, we discard the second solution.

Therefore, the length of the parallelepiped is 12 cm. The width is 5 cm less than the length, so the width is 12 - 5 = 7 cm. The smallest side length of the base is the width, which is 7 cm.

Answer

The smallest side length of the base of the rectangular parallelepiped is 7 cm.