The perimeter of a rectangle is 36 centimeters, the sum of the lengths of its three sides is 25 centimeters.

The perimeter of a rectangle is 36 centimeters, the sum of the lengths of its three sides is 25 centimeters. What is the area of this rectangle? Write down an explanation for each action.

In order to find the area of ​​a rectangle, you need to use the formula S = a * b.
But first you need to find the length and width, for this we substitute the known values ​​into the formula for finding the perimeter P = 2a + 2b:
36 = 25 + b.
Since the sum of the lengths of the three sides is known, we replaced two sides a and one side b by 25 cm.
Let’s transform the expression and find b:
b = 36 – 25 = 11.
Thus, the length is 11 cm.
Find the width value by substituting the values ​​into the same formula:
36 = 2a + 2 * 11;
36 = 2a + 22;
36 – 22 = 2a;
14 = 2a;
a = 7.
Now we substitute the known values ​​into the formula for finding the area and get the desired value:
S = 7 * 11 = 77 cm2.
Answer: 77 cm2.