The side of the square is 3 cm less than one of the sides of the rectangle and 2 cm

The side of the square is 3 cm less than one of the sides of the rectangle and 2 cm more than the other side. find the side of the square if you know that the area of the square is 30cm ^ 2 less than the area of the rectangle

1. Let the side of the square be “X”. Then the sides of the rectangle will be “X + 3” and “X – 2”. Let’s write expressions for the areas of a square and a rectangle:

Skv = X ^ 2;

Spr = (X + 3) * (X – 2).

2. Since the area of the square is 30cm ^ 2 less than the area of the rectangle, then we write:

Sq + 30 = Spr.

3. Let’s compose and solve the equation:

X^2 + 30 = (X + 3) * (X – 2);

X^2 + 30 = X^2 + 3X – 2X – 6;

X^2 + 3X – 2X – X^2 = 30 + 6;

X = 36 (cm).

Answer: the side of the square is 36 cm.