Find the area of a rectangle if its perimeter is 74 cm and the side difference is 17 cm.

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.