Final answer:
The false equation is option (d), where the area is calculated with a side length and a negative height, which is dimensionally inconsistent in geometry.
Step-by-step explanation:
The question asks which of the provided equations is dimensionally inconsistent or false in the context of geometry. We have four equations to examine.
- A = bh for h = b
- P = 2Cl + w for l = -w
- A = bh for h = b
- A = 2s + 4sh for h = -252
Upon review, option (a) A = bh is a standard equation for the area of a rectangle where h is the height and b is the base. When h = b, it reflects the special case of a square, which is still valid.
Option (b) P = 2Cl + w appears to be an equation for perimeter, where l = -w would indicate a shape with one pair of sides being the negative length of the other. This does not make practical sense in geometry as lengths cannot be negative.
Option (c) simply restates option (a) which is valid.
Option (d) lists A = 2s + 4sh where h = -252. This equation does not seem to represent a geometrically meaningful relationship for area, since area cannot be a function of a side length multiplied by an unrelated height, especially a negative one. Therefore, this is likely the dimensionally inconsistent equation.
The false equation is option (d), where negative height for area calculation does not make sense geometrically.