Question

Julie is constructing a scale model of her room.The rectangular room is 10 1/4 inches by 8 inches.If 1 inch represents 2 feet of the actual room,what is the scale factor and the actual area of the room?

Answer 1

The way to determine this is to know that 1 foot is 12 inches (so 2 is 24)
Now the ration that would determine the scale factor of the room is 1:24 (1 inch for every 24 inches)
So the scale factor is 1:24
Now to determine the area we multiply the numbers we have by 2 and change the inches to feet (I hope that makes sense to you, it does to me, I'll show you)
10.25 * 2 = 20.5 ft.
8 * 2 = 16 ft.
now we know the dimensions of the room so we need to find the area.
A=B*H
20.5 * 16 = 328
so the area of the room is 328 ft.²

Answer 2

328 square feet.

Explanation:

Julie is constructing a scale model of her room.

The model of the rectangular room is
`10(1)/(4)` inches by 8 inches.

The scale factor of the model is 1 inch = 2 feet.

The actual length of the room =
`10(1)/(4)` × 2

=
`(41)/(4)` × 2

=
`(41)/(2)`

=
`20(1)/(2)` feet

= 20.5 feet

The actual width of the room = 8 × 2

= 16 feet.

The actual size of the room is 20.5 feet by 16 feet.

Area = Length × width

Area of the room = 20.5 × 16

= 328 feet²

actual area 328 square feet and scale factor is 1 inch = 2 feet.