Would I have to change 16m into cm? And what is the height of the building?

Question

On a sunny day, Robert notices the length of the shadow of a building is 16m. Robert’s height is 175cm, and the length of his shadow is 114cm. What is the height of the building?

Answer 1

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You do not have to convert the 16 m into cm.  Since the conversion from m to cm would be the same either way, they cancel out when you convert them to a ratio.

If you set up a ratio of height to shadow length, Robert's ratio is:

175/114

(both have a label of "cm" resulting in the labels to cancel out so this ratio is dimensionless.)

The same ratio (in meters) for the building with an unknown height is:

x/16

Again, if both labels are meters, the cancel out so this ratio is dimensionless.  Since both ratios are equally dimensionless we can set them equal into a proportion to solve for the unknown.

175/114 = x/16

114x = 175 * 16

114x = 2800

x = 24.56 m (rounded to 2DP)

Answer 2

you have to be consistent, either m or cm, in each fraction. cm/cm or m/m or inches/inches, the units cancel, it is a proportion.

proportions

175/114 = x/16

x = 16•175/114 = ____ m

if I used all meters, that would be

1.75/1.14 = x/16

same thing.