The perimeter of the rectangle is 30 cm. Find its sides if it is known that the area of the rectangle is 56 cm2.

Perimeter (Ppr) = 30 cm;

Spr = 56 cm ^ 2;

Length (a) -? cm;

Width (b) -? cm;

The perimeter of a given rectangle is found by the formula:

Ppr = (a + b) * 2 = 30 (1).

The area of ​​the rectangle is determined by the ratio:

Spr = a * b = 56 (2).

From (1) the perimeter formula, we express b:

(a + b) * 2 = 30;

a + b = 15;

b = 15 – a.

Now we substitute the resulting expression into the formula for finding the area of ​​a rectangle:

a * (15 – a) = 56;

15a – a ^ 2 = 56;

a ^ 2 – 15a + 56 = 0;

D = (-15) ^ 2 – 4 * 1 * 56 = 225 – 224 = 1; sqrt (D) = ± 1.

a1 = (15 +1) / 2 = 8 (cm);

a2 = (15 -1) / 2 = 7 (cm).

Substituting the resulting value of one of the sides of the rectangle into the expression for finding the other side, we get:

b1 = 15 – a = 15 – 7 = 8 (cm);

b2 = 15 – a = 15 – 8 = 7 (cm).

Answer: the sides of the rectangle are 7 cm and 8 cm.