# The perimeter of the rectangle is 38 cm, width is 9 cm. Find the length of the rectangle.

The perimeter of the rectangle is 38 cm, width is 9 cm.

Let’s write down the known values:

Given a rectangle;
The perimeter of the rectangle is P = 38 cm;
The width of the rectangle is 9 cm.
Find the length of the rectangle
Let’s write the formula for the perimeter of a rectangle:

P = 2 * (a + b), where a and b are the sides of the rectangle.

We know that P = 38 cm, b = 9 cm. Find the length of the rectangle a.

In order to find the length of the rectangle, you need to substitute the known values ​​into the formula for the perimeter of the rectangle and calculate its value. That is, we get:

38 = 2 * (a cm + 9 cm).

38 = 2 * (a + 9);

Solve the equation 38 = 2 * (a + 9)
38 = 2 * (a + 9);

We expand the brackets. To do this, the value in front of the brackets, we multiply by each value in the brackets, and add them in accordance with their signs. Then we get:

38 = 2 * a + 2 * 9;

38 = 2 * a + 18;

Move all the values ​​of the expression to one side. When transferring values, their signs are changed to the opposite sign. That is, we get:

2 * a + 18 – 38 = 0;

2 * a – (38 – 18) = 0;

2 * a – 20 = 0;

Let’s take the common factor out of the brackets and then we get:

2 * (a – 10) = 0;

(a – 10) = 0;

We expand the brackets. Since there is a plus sign in front of the parentheses, when it is expanded, the value signs remain unchanged. That is, we get:

a – 10 = 0;

In order to solve the equation, we determine what properties the equation has:

The equation is linear and is written as a * x + b = 0, where a and b are any numbers;
For a = b = 0, the equation has an infinite set of solutions;
If a = 0, b ≠ 0, the equation has no solution;
If a ≠ 0, b = 0, the equation has a solution: x = 0;
If, a and b are any numbers other than 0, then the root is found by the following formula x = – b / a.
Since, a = 1 and b = – 10, then we find the root of the equation by the formula x = – b / a.

a = – (- 10) / 1;

a = 10/1;

a = 10;

From this, we got that the length of the rectangle is 10 cm.

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