The area of the rectangle is 4, the perimeter is 10, find the smaller side of the rectangle.

1. A, B, C, D – the vertices of the rectangle.

2. We take the length of AB as x, and the length of AD as y.

3. Let’s compose two equations:

xy = 4;

2 (x + y) = 10; x + y = 5; x = 5 – y;

4. Substitute x = 5 – y in the first equation:

(5-y) y = 4;

5y – y² – 4 = 0;

y² – 5y + 4 = 0;

The first value of y = (5 + √25 – 16) / 2 = (5 + 3) / 2 = 4;

The second value is y = (5 – 3) / 2 – 1.

AB = 1 unit or AB = 4 units.

AD = 4 units or AD = 1 unit.

Answer: the length of the shorter side is 1 unit.