The perimeter of the rectangle is 20cm. Find its sides if you know that the area of the rectangle is 24cm2.

1. Vertices of rectangle A, B, C, D.

2. We take the length of the side CD as x, the length of the side AD as y.

3. Let’s compose two equations:

(1) 2x + 2y = 20; x + y = 10; x = 10 – y;

(2) xy = 24;

4. Substitute the value x = (10 -y) into the second equation:

(10 – y) y = 24;

10y – y² = 24;

y² – 10y + 24 = 0;

The first value y = (10 + √100 – 24 x 4) 2 = 10 + √ (100 – 96) / 2 = 6 cm.

The second value is y = 10 – 2 = 4 cm.

The first value is x = 10 – 6 = 4 cm.

The second value is x = 10 – 4 = 6 cm.

5. The length of the CD side can be 4 cm or 6 cm.

Side length AD can be 6 cm or 4 cm.

Answer: the length of the CD side can be 4 cm or 6 cm, the length of the AD side can be 6 cm or 4 cm.