Question

Roxiand Jan constructed a scale model of a swing set. The height of the actual swing set is 10 feet tall and 15 feet long and 8.5 feet wide. Roxi crafts a swing set that is 25 in by 37.5 in by 21.25 in. What is the scale factor of Roxi's model? (Round to the nearest hundredth, if necessary)

Answer 1

The scale factor of Roxi's model is 5:24 ( ≅ 0.21).

Explanation:

A scale factor can be used to either enlarge or reduce the size of an object.

scale factor =
`(reduced length)/(actual length)`

Since 1 feet = 12 inches, then for the actual swing set;

length = 15 feet = 15 x 12 = 180 inches

height = 10 feet = 10 x 12 = 120 inches

width = 8.5 feet = 8.5 x 12 = 102 inches

For Roxi's crafts swing set;

length = 37.5 inches

height = 25 inches

width = 21.25 inches

i. Comparing the actual length with the length of Roxi's model.

scale factor of Roxi's model =
`(37.5)/(180)`

=
`(5)/(24)`

ii. Comparing the actual height with the height of Roxi's model.

scale factor of Roxi's model =
`(25)/(120)`

=
`(5)/(24)`

iii. Comparing the actual width with the width of Roxi's model.

scale factor of Roxi's model =
`(21.25)/(102)`

=
`(5)/(24)`

Therefore, the scale factor of Roxi's model is 5:24 ( ≅ 0.21).