Area of a Rhombus

Let the lengths of the semi-diagonals be $3x$ and $4x$. Since the diagonals of a rhombus intersect at right angles: $(3x)^2 + (4x)^2 = 15^2 \implies 25x^2 = 225 \implies x = 3$

So the semi-diagonals are $9\text{ cm}$ and $12\text{ cm}$, which means the full diagonals are $d_1 = 18\text{ cm}$ and $d_2 = 24\text{ cm}$.

$\text{Area} = \frac{1}{2} \times d_1 \times d_2 = \frac{1}{2} \times 18 \times 24 = 216\text{ sq. cm}$

Since $216\text{ sq. cm}$ is not among options A, B, C, D, the correct choice is Option E.