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

1. The formula for the perimeter of a rectangle is P = 2 * (a + b). Let us express b in terms of a:

20 = 2 * (a + b);

a + b = 10;

b = 10 – a.

2. The area formula for a rectangle S = a * b. Substitute the values and solve the resulting equation:

24 = a * (10 – a);

10a – a2 – 24 = 0;

a2 -10a + 24 = 0;

D = 100 – 96 = 4;

a1 = (10 + 2) / 2 = 6;

a2 = (10 – 2) / 2 = 4;

b1 = 10 – 6 = 4;

b2 = 10 – 4 = 6.

Answer: the sides of the rectangle are 6 cm and 4 cm.