Let one of the sides of the rectangle be x, the other – y.
The sum of the lengths of two adjacent sides is equal to half the perimeter, which means:
x + y = 74/2 = 37.
Knowing that the difference between the sides is 17 cm, we can write:
x – y = 17.
We have a system of equations:
1) x + y = 37;
2) x – y = 17.
Adding the left and right sides of these equations, we get:
2x = 54.
Hence, one of the sides of this rectangle is equal to:
x = 54/2 = 27 cm.
From the first equation:
y = 37 – x = 37 – 27 = 10 cm.
The area of a rectangle is equal to the product of its two adjacent sides:
S = x * y = 27 * 10 = 270 cm2.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.