The perimeter of the rectangle is 36 dm, the base is 6 cm more than the height. Find the sides of the rectangle.

First, let’s say what a perimeter is. The perimeter of a rectangle is the sum of its length and width multiplied by 2. That is, in the form of a formula, this definition will look like this:

P = 2 * (a + b)

where a is the length of the rectangle,
b is the width of the rectangle.

From the problem statement, we know that the length (in our case, the base) is 6 centimeters greater than the height (in our case, the width). Mathematically, this will take the form:

a = 6 + b

Then the formula for determining the perimeter will take the form:

P = 2 * (a + b) = 2 * (6 + b + b) = 2 * (2 * b + 6) = 4 * b + 12

From the condition we know that P = 36 dm = 360 cm.Toga:

4 * b + 12 = 360
b + 3 = 90
b = 90-3
b = 87 cm

Consequently:

a = 6 + b = 6 + 87 = 93 cm

So the length (base) of the rectangle is 93 centimeters, and the width (height) is 87 centimeters.