Question

В прямоугольном параллелепипеде длина в 3 раза больше ширины и в 2 раза меньше высоты. Найдите измерения прямоугольного параллелепипеда, если площадь его поверхности равна 864 см2. Помогите решить пожалуйста!!!

Answer 1

ширина Х 
длина 3*Х 
высота 6*Х 
площадь поверхности = 2(высота*длина+высота*ширина+длина*ширина) = 2*(3+6+18)*Х*Х=54*Х*Х 
и Х*Х = 16, отсюда Х = 4 
ответ: ширина = 4, длина = 12, высота = 24 

Answer 2

I will answer in detail. In a rectangular parallelepiped, the length is 3 times the width and 2 times smaller than the height. Find the dimensions of the rectangular parallelepiped if its surface area is equal to 864 cm2. Help me solve it please!!!

To solve this problem, we need to use the formulas for the surface area and the volume of a rectangular parallelepiped. Let x be the width, 3x be the length, and 6x be the height of the parallelepiped. Then, the surface area S is given by:

$$S = 2(lw + lh + wh)$$

Substituting the values of l, w, and h, we get:

$$S = 2(3x^2 + 18x^2 + 6x^2)$$

Simplifying, we get:

$$S = 54x^2$$

Since we are given that S = 864 cm2, we can equate the two expressions and solve for x:

$$54x^2 = 864$$

Dividing both sides by 54, we get:

$$x^2 = 16$$

Taking the square root of both sides, we get:

$$x = \pm 4$$

Since x is a length, we only take the positive value. Therefore, x = 4 cm. Then, the length is 3x = 12 cm, and the height is 6x = 24 cm.

The dimensions of the rectangular parallelepiped are 4 cm by 12 cm by 24 cm.