# In a rectangle, one side of which is twice as large as the other, all four sides have been increased by 1.

In a rectangle, one side of which is twice as large as the other, all four sides have been increased by 1. At the same time, its area has increased by 32 percent. By what percentage the smaller side has increased.

Legend:
a – the length of our rectangle;
b is the width of our rectangle.
Let’s write the condition in mathematical form.
a = 2 * b.
a + 1 – the length of the new rectangle;
b + 1 is the width of the new rectangle.
(a + 1) * (b + 1) = 1.32 * S1.
Now let’s make the equations and solve them.
S1 = a * b = 2 * b * b = 2 * b2.
S2 = (a + 1) * (b + 1) = (2 * b + 1) * (b + 1).
(2 * b + 1) * (b + 1) = 1.32 * 2 * b2;
(2 * b + 1) * (b + 1) = 2.64 * b2;
2 * b2 + 2 * b + b + 1 = 2.64 * b2;
0.64 * b2 – 3 * b – 1 = 0;
b = 5.34.
Answer: The width of the new rectangle is 5.34 centimeters.

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.