Question

On a blueprint, the scale indicates that 7 cm represent 16 ft. What is the length of a room that is 9.8 cm long and 5 cm wide on the blueprint

Answer 1

Multiply the measurements from the blueprint by the ratio 16 ft / 7 cm. Make sure that the units cancel properly.

For example, a 14 cm dimension on the blueprint:

\[14 \cancel{\text{ [cm]}} * \frac{16\text{ [ft]}}{7 \cancel{\text{ [cm]}}} = 32 \text{ [ft]}\]

If the units do not cancel properly, you've set up the conversion wrong, or made some other error.

We can convert the units this way because we are just multiplying by 1 in fractional form:

\[7 \text{ [cm]} = 16 \text{ [ft]}\]Divide both sides by 7 cm
\[1 = \frac{16 \text{ [ft]}}{7 \text{ [cm]} }\]