An architect is using the blueprint shown below where the side length of each grid square represents 12 inches.
We are asked if it would be possible to wheel a laundry cart that is 3 12 feet wide through the room from the doorway at the left to the doorway at the right. We can start by finding the scale of the blueprint.
Blueprint's scale &= $1$ Grid side length/$12$ inches
Notice that the narrowest part through which the laundry cart would have to go is 3 grid side lengths.
As the blueprint is drawn to scale, all the lengths will keep the same ratio with their actual corresponding lengths l .
Side length/Actual length &= $3$ Side lengths/Actual corresponding length
1/12 &= 3/l
We can now solve for the narrowest length l.
Hence, the actual measurement at the narrowest part would be 36 inches. Recall that the laundry cart is 3 12 feet wide. Let's convert the length of the laundry cart from feet to inches, multiplying by a conversion factor.
3 12 ft = 3.5 ft ( 12 in/1 ft ) = 42 in
Since the narrowest part measures at only 36 inches, the laundry cart will not fit. It will not be possible to wheel it through the room from doorway to doorway.
