Question

$\left[{\mathbf{L}}^{\mathbf{2}}\right]$represents the dimensions for which of the following?

(a) cm²

(b) square feet

(c) m²

(d) All the above

Short answer

The correct option is (d).

Step-by-step solution

Step 1. Relation between the length and area 

The dimension of any quantity is defined as the extent of the measurement of a particular kind. There are three fundamental dimensions with the help of which the others are derived.

You know that the dimension of the length is $\left[\mathrm{L}\right]$. You also know that $\mathrm{Area}={\left(\mathrm{Length}\right)}^2$.

Step 2. Calculation of the dimension of the area

The dimension of the area is

$\begin{array}{l}A=\left[\mathrm{L}\right]\left[\mathrm{L}\right]\\ A=\left[{\mathrm{L}}^2\right]\end{array}$

Here, all the given options (cm², square feet, and m²) represent the unit of the area.

Therefore, the answer will be that all the given options have the dimension $\left[{\mathrm{L}}^2\right]$.