If you are to calculate the hypotenuse of a triangle, the formula is: h = x 2 + y 2 If you don't have any units for the numbers, replacing x and y is pretty straightforward: h = 4 2 + 6 2 But what if the numbers are in meters? h = 4 2 m + 6 2 m (wrong, would become 52 m ) h = 4 m 2 + 6 m 2 (wrong, would become 10 m 2 ) h = ( 4 m ) 2 + ( 6 m ) 2 (correct, would become 52 m 2 )Or should I just ignore the unit of measurement in these cases?

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If you are to calculate the hypotenuse of a triangle, the formula is:  h  =            x      2        +          y      2      If you don&#039;t have any units for the numbers, replacing x and y is pretty straightforward:   h  =            4      2        +          6      2      But what if the numbers are in meters?  h  =            4      2        m    +          6      2        m   (wrong, would become       52    m  )  h  =      4          m      2        +    6          m      2       (wrong, would become       10          m      2      )  h  =      (    4    m          )      2        +    (    6    m          )      2       (correct, would become       52          m      2      )Or should I just ignore the unit of measurement in these cases?

Belen Bentley · Accepted Answer

Suppose you have been given   x and   y in metres, and you&#039;d like to know the quantity,   z  =            x      2        +          y      2      . Then, as you have predicted this quatity will be in metres.Two things have been involved:Homogeneity of DimensionTwo quantities of different dimensions cannot be added. This is one of the axioms of numerical physics.Example: It is clear that adding 5 metres to 3 seconds does not give a physically meaningful quantity that can be interpreted in real life.Certain functions only take values in dimensionless quantitiesFor instance,   sin  ⁡  (            x      2        +          y      2        ) would not make sense even if   x and   y have same dimensions. This is a bit subtler, but this is what it is!1. Coming to your question, the first quantity you tell us in dimension of       m          1              /            2       which is against your guess!2. The second quantity is dimensionally fine while numerically this is not what you want.3. The third quantity is fine in all ways.My suggestion:First manipulate the numbers and then the units separately. This is a good practice in Numerical Physics. The other answers have done it all at one go. But, I don&#039;t prefer it that way!

freakygirl838w · Accepted Answer

The last one:                    h                            =                  (          4           m                      )            2                    +          (          6           m                      )            2                                                            =                  16                       m            2                    +          36                       m            2                                                            =                  52                       m            2                                                            =        2                  13                 m

If you are to calculate the hypotenuse of a triangle, the formula is: h = <msqrt>

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