Question

An architect is printing a blueprint for a building they just finished designing. On the

blueprint, the length and width of one of the rooms is 18 inches by 16 inches. When
the room is built, it will be 28 feet 6 inches by 25 feet 4 inches.
What is the scale factor that dilates the blueprint to the size of the built room?
CHECK ANSWER

Answer 1

the scale factor that dilates the blueprint to the size of the built room is 19.

Explanation:

To find the scale factor that dilates the blueprint to the size of the built room, we need to compare the corresponding dimensions of the blueprint and the actual room.

The blueprint shows the length and width of the room as 18 inches by 16 inches. The actual room dimensions are given as 28 feet 6 inches by 25 feet 4 inches.

First, we need to convert the dimensions of the actual room to inches for consistency.

28 feet 6 inches can be converted to inches by multiplying 28 by 12 (since there are 12 inches in a foot) and adding 6 inches.

28 feet * 12 inches/foot + 6 inches = 336 inches + 6 inches = 342 inches

Similarly, 25 feet 4 inches can be converted to inches:

25 feet * 12 inches/foot + 4 inches = 300 inches + 4 inches = 304 inches

Now we can compare the dimensions of the blueprint (18 inches by 16 inches) to the actual room dimensions (342 inches by 304 inches).

To find the scale factor, we divide the corresponding dimensions of the actual room by the corresponding dimensions of the blueprint.

Scale factor for length: 342 inches (actual room) / 18 inches (blueprint) = 19

Scale factor for width: 304 inches (actual room) / 16 inches (blueprint) = 19

Therefore, the scale factor that dilates the blueprint to the size of the built room is 19.