Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

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

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?

Relevance

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)

• 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.