A scale drawing of the floor of a theater has a scale factor of 18. Mark says that he can use this information and any length on the scale drawing to find the corresponding length and the actual theater. He says that he can also use this information and any length in the actual theater to find the corresponding length on the scale drawing. Is Mark correct? I really don't understand. I would really appreciate help.

Question

Thank you!

Answer 1

Do you know what a scale factor is?
e.g. there are 12 inches in a foot

so if we have a patio which is 10 ft by 14 ft, I could make a drawing where 1 inch repesents 1 foot. My scale factor is 12
so I would draw my patio as 10 inches by 14 inches

In our case the scale factor is 18
so 1 unit on the paper sketch would be 18 units in reality.
so if Mark sketched a room as 8 inches by 10 inches, then the actual dimensions of the room would be
8(18)inches by 10(18) inches
= 144 inches by 180 inches
= 12 ft by 15 ft

to go from the real world down to a sketch, we would divide the dimensions by the scale factor