The perimeter of the rectangle is 32. Find the sides of the rectangle if the difference between the adjacent sides is 2.

Find the sum of the sides of the rectangle:
a + b = 32: 2;
a + b = 16;
We compose a system of equations:

{a + b = 16,
{a – b = 2.

Express one side through the other:

{a = 16 – b,
{a – b = 2.

We substitute the first equation into the second:

{a = 16 – b,
{16 – b – b = 2.

We solve the second equation:
16 – b – b = 2;
16 – 2b = 2;
16 – 2 = 2b;
2b = 14;
b = 14: 2;
b = 7 cm – the width of the rectangle.
Let’s calculate the length of the rectangle:
a = 16 – b;
a = 16 – 7;
a = 9 cm – the length of the rectangle.
Answer: 7 cm and 9 cm.