The length of the rectangle is 5 cm longer than the side of the square and its width is 2 cm less than the side of the square.

The length of the rectangle is 5 cm longer than the side of the square and its width is 2 cm less than the side of the square. Find the area of a square if it is known that it is 32 cm in a square less than the area of a rectangle.

1. Let the side of the square be u cm. Then the length and width of the rectangle are equal, respectively:

v = u + 5;
w = u – 2.
2. By the condition of the problem, the area of the rectangle is 32 cm ^ 2 larger than the area of the square:

vw = u ^ 2 + 32;
(u + 5) (u – 2) = u ^ 2 + 32.
3. Let’s open the brackets and solve the equation:

u ^ 2 – 2u + 5u – 10 = u ^ 2 + 32;
3u = u ^ 2 + 32 – u ^ 2 + 10;
3u = 42;
u = 42: 3;
u = 14 (cm).
4. The area of the square is:

S = u ^ 2 = 14 ^ 2 = 196 (cm ^ 2).

Answer: 196 cm ^ 2.