Find the sides of a rectangle if its area = 45 cm2, and the perimeter is 28 cm do it using the leveling system

Let’s denote the sides of the rectangle by x and y. Then its area is x * y. And by condition, it is equal to 45 cm ^ 2. We get the first equation:

x * y = 45.

By condition, we also know the perimeter of the rectangle, then we get the second equation:

2 * (x + y) = 28.

Reduce both sides of the equality by 2, we get:

x + y = 14.

From this equation we find x:

x = 14 – y and substitute in the first equation instead of x its value, we get:

(14 – y) * y = 45;

14y – y ^ 2 – 45 = 0;

y ^ 2 – 14y + 45 = 0;

Let’s find the discriminant of the equation:

D = 14 ^ 2 – 4 * 1 * 45 = 196 – 180 = 16.

y1 = (14 + 4) / 2 = 18/2 = 9;

y2 = (14 – 4) / 2 = 10/2 = 5.

Find the second side of the rectangle:

x1 = 14 – y1 = 14 – 9 = 5;

x2 = 14 – y2 = 14 – 5 = 9.

So if the length is 9 cm, then the width is 5 cm and vice versa.

Answer: the sides of the rectangle are 9 cm and 5 cm.