Question

Suppose your living room measures 16 ft by 20 ft. If you wish to make a scale drawing of the room, and the shorter side of the room is 12 in, the longer side will be:

a) 15 in
b) 18 in
c) 24 in
d) 30 in

Answer 1

The correct scale length for the longer side of the room is 15 inches when using a scale factor determined by the given dimensions and the scale length of the shorter side.

Step-by-step explanation:

To determine the scale length of the longer side of the living room in a drawing, given that the shorter side (16 ft in actual size) is represented as 12 in on the scale drawing, we must first calculate the scale factor. To find this, we divide the scale length by the actual length: 12 in (scale) / 16 ft (actual).

Since 1 ft = 12 in, the actual length in inches is 16 ft x 12 in/ft = 192 in. Therefore, the scale factor is 12 in / 192 in = 1/16. Now, we can apply this scale factor to the longer side, which is 20 ft in actual length. Converting this to inches gives us 20 ft x 12 in/ft = 240 in. Multiplying the actual length of the longer side by the scale factor provides the length of the longer side in the scale drawing: 240 in x (1/16) = 15 in.