Question

Висота прямокутного паралелепіпеда дорівнює 15см, що на 5 см більше за ширину і у 2 рази менше від довжини. Знайди суму довжин усіх ребер паралелепіпеда та площу його поверхні.

Answer 1

Ответ: 300 см в квадрате площадь поверхности (сорян, я сам забыл что такое ребро у фигур :( )

Решение :

1) 15 - 5 = 10 (ширина)

2)15 × 2 = 30 (длина)

3)10 × 30 = 300 (см в квадрате)

Answer 2

Calculation of the Dimensions:

To find the sum of the lengths of all the edges of the rectangular parallelepiped and the surface area, we first need to determine the dimensions of the parallelepiped based on the given information.

Let's denote the width of the parallelepiped as w, the height as h, and the length as l.

According to the given information: - The height of the parallelepiped is 15 cm. - The height is 5 cm more than the width: h = w + 5. - The height is 2 times smaller than the length: h = l/2.

We can use these equations to solve for the dimensions of the parallelepiped.

Substituting the third equation into the second equation, we get: l/2 = w + 5.

Simplifying the equation, we have: l = 2w + 10.

Substituting the second equation into the first equation, we get: w + 5 = 15.

Simplifying the equation, we have: w = 10.

Using this value of w, we can find the values of h and l: h = 10 + 5 = 15, l = 2(10) + 10 = 30.

Therefore, the width of the parallelepiped is 10 cm, the height is 15 cm, and the length is 30 cm.

Calculation of the Sum of Edge Lengths:

The sum of the lengths of all the edges of a rectangular parallelepiped can be calculated using the formula: Sum of Edge Lengths = 4(l + w + h).

Substituting the values we found earlier, we have: Sum of Edge Lengths = 4(30 + 10 + 15) = 4(55) = 220 cm.

Therefore, the sum of the lengths of all the edges of the parallelepiped is 220 cm.

Calculation of the Surface Area:

The surface area of a rectangular parallelepiped can be calculated using the formula: Surface Area = 2lw + 2lh + 2wh.

Substituting the values we found earlier, we have: Surface Area = 2(30)(10) + 2(30)(15) + 2(10)(15) = 600 + 900 + 300 = 1800 cm².

Therefore, the surface area of the parallelepiped is 1800 cm².

In summary: - The sum of the lengths of all the edges of the parallelepiped is 220 cm. - The surface area of the parallelepiped is 1800 cm².