Two similar triangles of ΔXYZ and ΔLMN. If area of (ΔXYZ) = 16 cm², area of (ΔLMN) = 25 cm² and YZ = 2.4 cm, then the measure of MN is:

The correct option is 3 cm.

To find the measure of side $\mathrm{MN}$ in the triangle $\Delta \mathrm{LMN}$, we can use the theorem regarding the areas of similar triangles.
The area theorem for similar triangles states that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Given:
- $\Delta \mathrm{XYZ}~\Delta \mathrm{LMN}$
- Area of $\Delta \mathrm{XYZ}=16{\mathrm{cm}}^2$
- Area of $\Delta \mathrm{LMN}=25{\mathrm{cm}}^2$
- $\mathrm{YZ}=2.4\mathrm{cm}$ (where $\mathrm{YZ}$ and $\mathrm{MN}$ are corresponding sides of the similar triangles)

Using the area theorem:
$\frac{\text{Area of}\Delta \mathrm{XYZ}}{\text{Area of}\Delta \mathrm{LMN}}={\left(\frac{\mathrm{YZ}}{\mathrm{MN}}\right)}^2$

Substituting the given values into the formula:
$\frac{16}{25}={\left(\frac{2.4}{\mathrm{MN}}\right)}^2$

Taking the square root on both sides to solve for $\mathrm{MN}$:
$\sqrt{\frac{16}{25}}=\frac{2.4}{\mathrm{MN}}$

$\frac{4}{5}=\frac{2.4}{\mathrm{MN}}$

Now, cross-multiply to isolate $\mathrm{MN}$:
$4·\mathrm{MN}=2.4·5$

$4·\mathrm{MN}=12$

$\mathrm{MN}=\frac{12}{4}$

$\mathrm{MN}=3\mathrm{cm}$

Therefore, the measure of side $\mathrm{MN}$ is $3\mathrm{cm}$.