The perimeter of the rectangle is 18cm and its area is 20cm ^ 2. find the sides of the triangle.

We are given a rectangle with a perimeter of 18 centimeters and an area of ​​20 centimeters², we need to find its sides, let’s start solving:

Since the lengths and widths in a rectangle are equal to each other, we mark the length as the letter a, and the width as the letter b;

The perimeter of the rectangle can be found by the formula 2 * (a + b), and the area of ​​the rectangle by the formula a * b, then if we know that the perimeter is 18 and the area is 20, we will compose a system of equations and solve it:

{2 * (a + b) = 18;
{a * b = 20;

{2a + 2b = 18;
{a * b = 20;

{a = 20 / b;
{2 * 20 / b + 2b = 18;

{a = 20 / b;
{b² – 9b + 20 = 0;

b² – 9b + 20 = 0
D = 81 – 4 * 20 * 1;
D = 1

b (1) = 5, then a (1) = 4, but since the length is always greater than the width, this option is impossible

b (2) = 4, then a (2) = 5, the answer suits us

Answer: the length is 5 centimeters and the width is 4 centimeters