Identify Given Parameters

We are given the length $l = 12$ cm and the diagonal $d = 13$ cm of the rectangle.

$l = 12\text{ cm}, \quad d = 13\text{ cm}$

Find the Breadth Using Pythagoras Theorem

The relationship between length, breadth, and diagonal of a rectangle is given by $d^2 = l^2 + b^2$. Substituting the values: $13^2 = 12^2 + b^2$.

$169 = 144 + b^2$

Calculate the Breadth

Solving for $b^2$, we get $b^2 = 169 - 144 = 25$. Therefore, the breadth $b = 5$ cm.

$b = \sqrt{25} = 5\text{ cm}$

Calculate the Area of the Rectangle

The area of a rectangle is the product of its length and breadth: $\text{Area} = l \times b = 12 \times 5$.

$\text{Area} = 12 \times 5 = 60\text{ sq cm}$