The sides of the rectangle are 9: 1, and their difference is 32 cm, find the area of the rectangle.

The sides of the rectangle are 9: 1, and their difference is 32 cm, find the area of the rectangle. Find the side of the square, the area of which is equal to the area of the rectangle.

1. Vertices of the rectangle A, B, C, D. AD / AB = 9/1. AD – AB = 32 cm. S – area of the rectangle.

2. By the condition of the problem AD / AB = 9/1. Therefore, AD = 9AB.

3. AD – AB = 32 cm (according to the problem statement).

4. Substitute in this expression 9AB instead of AD:

9AB – AB = 32 cm.

8AB = 32 cm

AB = 4 cm.

AD = 9AB = 4 x 9 = 36 cm.

5. S = AB x AD = 4 x 36 = 144 cm².

6. Considering that the area of the square is also 144 cm², the length of the side of the square = √144 = 12 cm.

Answer: the length of the side of the square is 12 cm.