Question

Боковое ребро прямоугольного параллелепипеда 6 см.диагональ в два раза меньше за периметр основи.Найти площу основи Бічне ребро прямокутного паралелепіпеда 6 см. ,діагональ паралелепіпеда в двічі менша за периметр основи.Знайдіть площину основиПОМОГИТЕ ПЛЗ!!!

Answer 1

Problem Analysis

We are given the following information: - The length of the lateral edge of a rectangular parallelepiped is 6 cm. - The diagonal is twice as small as the perimeter of the base.

We need to find the area of the base.

Solution

Let's assume the length, width, and height of the rectangular parallelepiped are L, W, and H, respectively.

From the given information, we can deduce the following equations: 1. The lateral edge of the parallelepiped is 6 cm: L + W + H = 6. 2. The diagonal is twice as small as the perimeter of the base: 2(L + W) = 2H.

To find the area of the base, we need to know the dimensions of the base. Let's solve the equations to find the values of L, W, and H.

From equation 2, we can rewrite it as L + W = H.

Substituting this value in equation 1, we get 2H + H = 6.

Simplifying the equation, we have 3H = 6.

Dividing both sides by 3, we find H = 2.

Substituting this value in equation 2, we get L + W = 2.

Now we have two equations: 1. L + W + H = 6 2. L + W = 2

Subtracting equation 2 from equation 1, we get H = 4.

Substituting this value in equation 2, we find L + W = 2.

Now we have three equations: 1. L + W + H = 6 2. L + W = 2 3. H = 4

Solving these equations, we find L = 1, W = 1, and H = 4.

The area of the base is given by L * W = 1 * 1 = 1 square cm.

Therefore, the area of the base of the rectangular parallelepiped is 1 square cm.

Summary

The area of the base of the rectangular parallelepiped is 1 square cm.