# The perimeter of the rectangle is 32 cm. Find the sides of the rectangle if its area is 39 cm2.

January 13, 2021 | education

| Given:

Rectangle;

Perimeter = 32 cm;

Area = 39 cm ^ 2;

Find the sides of a rectangle;

Decision:

Let x be one side of the rectangle;

y – the other side of the rectangle, not equal to the side x;

Since, perimeter = 2 * (x + y), and area = x * y;

Then, substituting the known values, we get:

32 = 2 * (x + y);

39 = x * y;

We got a system of equations:

Let’s solve it and find x and y.

1) From the first 32 = 2 * (x + y);

x + y = 32/2;

x + y = 16;

x = 16 – y;

2) Substitute in the second equation:

39 = x * y;

39 = (16 – y) * y;

39 = 16 * y – y ^ 2;

39 – 16 * y + y ^ 2 = 0;

Hence, y1 = 3 and y2 = 13;

3) x1 = 16 – y1 = 16 – 3 = 13;

x2 = 16 -y2 = 16 – 13 = 3;

This means that the sides of the rectangle are 3 cm and 13 cm.

Answer: 3 cm and 13 cm.

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.