Question

valuate [r]; i.e., the units of r, in the expression
r =
squareroot of (s − a) (s − b) (s − c)
over s
,
where s =
1/2(a + b + c), and a, b, and c have
units of meters.

Answer 1

1D-line
2D- area
3D - volume
when you add or substract some numbers with the same unit it's like you just add or substract some intervals in coordinate system e.g.
even adding vectors gives you one dimensional object
so s has also unit of meter(multiplying, dividing, adding or substracting by number(dimensionless object) doesn't change the unit of object)
but when you multiply two objects with same unit you get 2D object and so on e.g.
an so on
s has unit of meter
s-a , s-b, s-c have unit of meter, if you multiply and divide them you get m*m*m/m =m^2
square root of m^2 is simply m
so unit of r, [r]=[meter]