The area of the rectangle is 24 cm2. Could the perimeter of this rectangle be 24 cm?

Let one side of the rectangle be “a”. And the second side of the rectangle is “b”.

The area of such a rectangle is “a * b” and the perimeter is “2a + 2b”.

Knowing that the area is 24 sq. Cm, we express the “a” side:

a * b = 24;

a = 24 / b. (one)

Knowing that the perimeter is 24 cm, we get:

2a + 2b = 24. (2)

Let us put equation (1) in (2).

2 * 24 / b + 2b = 24;

48 / b + 2b = 24;

Let’s multiply both sides of the equation by “b”:

48 + 2b² = 24b;

2b² – 24b + 48 = 0;

D = 192;

b₁ = 6 + 2√3;

b₂ = 6 – 2√3;

We get 2 options for the rectangle:

1) a₁ = 24 / (6 + 2√3) and b₁ = 6 + 2√3.

2) a₂ = 24 / (6 – 2√3) and b₂ = 6 – 2√3.