The side of a square is 3 cm smaller than one of the sides of a rectangle and 2 cm greater than its other side. find the side of the square, if it’s known that the area of the square is 30 cm^2 less than the area of the rectangle.

36 cm

Let s represent the side of the square in cm. Then s+3 and s-2 are the sides of the rectangle of interest.

The area of the rectangle is the product of its side lengths:

... rectange area = (s+3)(s-2) = s² +s -6

The area of the square is the product of its side lengths, both of which are s.

... square area = s²

The difference of these areas is 30 cm², so ...

... rectangle area - square area = 30

... (s² +s -6) -(s²) = 30

... s = 36 . . . . . . . . . . . . simplify, add 6

The side of the square is 36 cm.

Check

The rectangle dimensions are 39 cm by 34 cm, so its area is

... (39 × 34) cm² = 1326 cm²

The area of the square is (36 cm)² = 1296 cm²

The difference in areas is (1326 -1296) cm² = 30 cm², as required.