Question

Полоска на рисунке составлена из x прямоугольников {где x любое целое число}Длинная сторона в 3 раза длиннее короткой.Короткая сторона равна a {где а,любое целое число} Найти P выразив его через x и aПомогите решить пожалуйста!

Answer 1

Problem Analysis

We are given a strip composed of x rectangles, where x is any integer. The length of the long side of each rectangle is three times the length of the short side. The short side is equal to a, where a is any integer. We need to find the perimeter P of the strip in terms of x and a.

Solution

To find the perimeter P of the strip, we need to calculate the sum of the lengths of all the sides of the rectangles.

Let's consider one rectangle in the strip. The length of the long side is three times the length of the short side. Therefore, the long side has a length of 3a, and the short side has a length of a.

Each rectangle has two long sides and two short sides. So, the total length of the sides of one rectangle is:

2 * (3a) + 2 * a = 6a + 2a = 8a

Since there are x rectangles in the strip, the total length of all the sides of the rectangles is:

8a * x = 8ax

Therefore, the perimeter P of the strip, expressed in terms of x and a, is:

P = 8ax

Example

Let's take an example to illustrate the solution. Suppose x = 5 and a = 2.

In this case, we have 5 rectangles in the strip, and the length of the short side of each rectangle is 2.

Using the formula P = 8ax, we can calculate the perimeter:

P = 8 * 5 * 2 = 80

Therefore, the perimeter of the strip is 80.

Conclusion

The perimeter P of the strip, composed of x rectangles with a short side length of a, can be expressed as P = 8ax.