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.