Define dimensions

Let the breadth of the rectangle be $B$. Given that the length $L$ is thrice the breadth, we have $L = 3B$.

$L = 3B$

Use perimeter formula

The perimeter of a rectangle is given by $P = 2(L + B)$. Substituting $48$ for $P$ and $3B$ for $L$:

$48 = 2(3B + B)$

Solve for Breadth (B)

Simplify the equation: $48 = 2(4B)$, which means $48 = 8B$. Dividing by $8$ gives $B = 6$.

$B = 6 \text{ cm}$

Calculate Length (L)

Using $L = 3B$, we find the length: $L = 3 \times 6 = 18$.

$L = 18 \text{ cm}$

Calculate Area (A)

The area is the product of length and breadth: $A = L \times B = 18 \times 6 = 108$.

$A = 108 \text{ cm}^2$