Question

\(\left( {{{\bf{L}}^{\bf{2}}}} \right)\)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

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 \(\left( {\rm{L}} \right)\). You also know that \({\rm{Area}} = {\left( {{\rm{Length}}} \right)^2}\).

Calculation of the dimension of the area

The dimension of the area is

\(\begin{aligned}{l}A = \left( {\rm{L}} \right)\left( {\rm{L}} \right)\\A = \left( {{{\rm{L}}^{\rm{2}}}} \right)\end{aligned}\).

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 \(\left( {{{\rm{L}}^{\rm{2}}}} \right)\).