Find the sides of the rectangle if its area is 3 dm squared and the perimeter is 8 dm.

In order to find the lengths of the sides of a rectangle, if its area is 3 dm ^ 2, and the perimeter is 8 dm, we compose and solve a system of equations.

Let’s recall the formula for finding the perimeter and area of ​​a rectangle.

P = 2 (a + b) – rectangle perimeter;

S = a * b – area of ​​the rectangle.

System of equations:

2 (a + b) = 8;

a * b = 3.

System of equations:

a + b = 4;

a * b = 3;

Let us express the variable a from the second equation through b.

System:

a + b = 4;

a = 3 / b;

System:

3 / b + b = 4;

a = 3 / b.

3 + b ^ 2 = 4b;

b ^ 2 – 4b + 3 = 0;

D = b ^ 2 – 4ac = 16 – 12 = 4;

b1 = (4 + 2) / 2 = 6/2 = 3;

b2 = (4 – 2) / 2 = 2/2 = 1.

A set of systems:

System 1:

b = 3;

a = 3/3 = 1;

System 2:

b = 1;

a = 3/1 = 3.

Answer: the sides are equal to 1 and 3 inches.