In a rectangle, one side is 7 cm longer than the other and the diagonal is 13 cm. Calculate the area of ​​the rectangle

Let one side of the rectangle be x cm, then the other side will be (x+7) cm.

We know that the diagonal of a rectangle forms a right triangle with the sides of the rectangle. So, we can use the Pythagorean theorem to find the relationship between the sides of the rectangle:

x^2 + (x+7)^2 = 13^2

Expanding and simplifying:

x^2 + x^2 + 14x + 49 = 169

2x^2 + 14x - 120 = 0

Dividing the equation by 2 to simplify:

x^2 + 7x - 60 = 0

Factoring the quadratic equation:

(x+12)(x-5) = 0

So, x = 5 cm (as the side length of a rectangle can't be negative).

Therefore, the sides of the rectangle are 5 cm and 12 cm.

The area of a rectangle is given by the formula: Area = length \times width

Therefore, the area of the rectangle is:

Area = 5 \times 12 = 60 \, cm^2

\boxed{60 \, cm^2} is the area of the rectangle.