# The diagonal of the rectangle is 30 dm, and its area is 432 dm2. Find the sides of the rectangle.

August 28, 2021 | education

| Let’s immediately introduce two variables to solve the problem.

Let the length of the rectangle be m, the width of the rectangle n.

Let’s compose and solve a system of two equations with two unknowns:

m ^ 2 + n ^ 2 = 900;

m * n = 432;

Using the method of algebraic addition, we add the first equation and the second, multiplied by two:

m ^ 2 + n ^ 2 + 2 * m * n = 900 + 864;

(m + n) ^ 2 = 1764;

m + n = 42;

We get from here:

n = 42 – m;

Substitute the expression for the variable into the second equation of the system:

m * (42 – m) – 432 = 0;

42 * m – m ^ 2 – 432 = 0;

m ^ 2 – 42 * m + 432 = 0;

m ^ 2 – 2 * m * 21 + 441 – 9 = 0;

(m – 21) ^ 2 = 9;

m1 – 21 = -9;

m2 – 21 = 9;

m1 = 12;

m2 = 30.

The sides of the rectangle are 12 and 30 in.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.