Find in the rectangle one side is 4 cm larger than the other, the area is 45 cm ^ 2, find the sides of the rectangle.

1. Let’s designate the sides of the rectangle ‘x’ and ‘y’ and compose equations according to the conditions of the problem:

{y – x = 4;
{xy = 45.

2. Let’s solve the system of equations by the substitution method:

{y = x + 4;
{xy = 45;
{y = x + 4;
{x (x + 4) = 45;
{y = x + 4;
{x ^ 2 + 4x – 45 = 0;
D / 4 = 2 ^ 2 + 45 = 49;

x = -2 ± √49 = -2 ± 7;

x1 = -2 – 7 = -9, does not make sense;
x2 = -2 + 7 = 5;
{y = x + 4;
{x = 5;
{y = 5 + 4;
{x = 5;
{y = 9;
{x = 5.
Answer: 5 cm and 9 cm.