Question

Сума довжин ребер прямокутного паралелепіпеда АВСDA1B1C1D1 дорівнює 80 м. Знайдіть довжини його ребер, якщо у нього один із вимірів на 3см більший за другий і на 20 см менший від третього. Розв'язання будь ласка!!!!!

Answer 1

Пусть ширина = х, тогда длина =х-3, высота=х+20. Так как в пар-де 4 высоты, 4 длины и 4 ширины, можно составить уравнение: 4(х-3)+4х+4(х+20)=8000. 12х=7908, х=659 (ширина) 659-3=656 (длина) 659+20=679 (высота)

Answer 2

Finding the Lengths of the Edges of the Rectangular Parallelepiped

To find the lengths of the edges of the rectangular parallelepiped, we can use the given information about the sum of the lengths of its edges and the relationships between its dimensions.

Let's denote the lengths of the edges as follows: - Length: l - Width: w - Height: h

The sum of the lengths of the edges of the rectangular parallelepiped is given as 80 m.

We are also given the relationships between its dimensions: - One dimension is 3 cm greater than the second dimension. - One dimension is 20 cm less than the third dimension.

Formulating the Equations

We can set up the following equations based on the given relationships: 1. l + w + h = 80 (sum of the lengths of the edges) 2. l = w + 3 (one dimension is 3 cm greater than the second dimension) 3. w = h - 20 (one dimension is 20 cm less than the third dimension)

Solving the Equations

We can solve this system of equations to find the lengths of the edges of the rectangular parallelepiped.

Substituting the expressions for l and w from equations 2 and 3 into equation 1: (w + 3) + w + (w + 20) = 80 3w + 23 = 80 3w = 57 w = 19

Using the value of w to find h: h = w + 20 h = 19 + 20 h = 39

Using the values of w and h to find l: l = w + 3 l = 19 + 3 l = 22

Answer

Therefore, the lengths of the edges of the rectangular parallelepiped are: - Length (l): 22 cm - Width (w): 19 cm - Height (h): 39 cm