Dimensional Consistency Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Is A=l+wA = l + w a valid formula for area?

Solution

  1. 1
    [l+w]=m+m=m[l + w] = \text{m} + \text{m} = \text{m}, but [A]=m2[A] = \text{m}^2.
  2. 2
    No — m≠m2\text{m} \neq \text{m}^2. The correct formula is A=lwA = lw.

Answer

No, dimensionally wrong.
Area has dimensions of length², but l+wl + w has dimensions of length¹. The correct formula A=lwA = lw gives m×m=m2\text{m} \times \text{m} = \text{m}^2.

About Dimensional Consistency

The principle that every term added or equated in a valid equation must share the same physical dimensions or units.

Learn more about Dimensional Consistency →

More Dimensional Consistency Examples

Example 1 easy

Is the equation [formula] (velocity = distance + time) dimensionally consistent?

Example 2 medium

Check: [formula] where [formula] is energy (kg·m²/s²), [formula] is mass (kg), [formula] is speed (m

Example 4 medium

In the equation [formula] (where [formula] is in meters), are all terms dimensionally consistent?

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