Question

Danielle is creating a scale drawing of her room. the rectangular room measures 20 1/2 by 25ft. if her drawing uses the scale where 1 inch represents 2 feet of the actual room,will her drawing fit on an 8 1/2 in. by 11 in. piece of paper?

Answer 1

NO, The drawing will be 10 1/4 inches by 12 inches, which is bigger than the paper.

Answer 2

Will not fit

Explanation:

Given:-

- The actual room dimension, R = ( 20.5 x 25 ) ft^2

- The scale used : 1 in ------> 2ft

- The available dimension of paper, P = ( 8.5 x 11 ) in^2

Find:-

- Will her drawing fit on paper for which the dimensions are given?

Solution:-

- We can use direct proportions to determine the dimensions of scale drawing of the room. Using the scale and actual dimensions as follows:

in ft

Scale: 1 2

Actual: x 20.5

- The scaled length of the room (x) can be calculated using direct proportions:

x = (20.5 ft)*(1 in) / ( 2 ft)

x = 10.25 in

- in ft

Scale: 1 2

Actual: y 25

- The scaled width of the room (y) can be calculated using direct proportions:

y = (25 ft)*(1 in) / ( 2 ft)

y = 12.5 in

- The dimensions of the scaled drawing of the room are:

( 10.25 x 12.5 )

- The available dimensions of the paper:

( 8.5 x 11 )

- We can conclude that:

( 10.25 x 12.5 ) > ( 8.5 x 11 )

The scaled drawing would be larger than the available paper. So the it would not fit!