An architect is recreating the blueprint for a deck with an existing scale factor of 1in.=2ft. Using 12in by 8in. The architect is using a different scale so that the length of the deck on the new blueprint measures 8 inches. What is the scale factor of the new blueprint? What is the width of the deck on the new blueprint?

New scale factor is 1 inch = 3 ft.

New width of the blueprint = (16/3) inches = 5.3333 inches

Step-by-step explanation:

Initial scale factor is 1 inch = 2 ft

And the architect draws a blueprint of 12 inches by 8 inches.

Converting to real life scale using 1 inch = 2 ft

Length = 12 inches = 12 × 2 ft = 24 ft

Width = 8 inches = 8 × 2 ft = 16 ft.

New scale factor turns the length to 8 inches

Scale factor = (length in the drawing)/(real life length)

Scale factor = (8 inches)/(24 ft) = (1 inch)/(3 ft)

Hence, new scale factor is 1 inch = 3 ft.

New width of the blue print

3 ft in real life = 1 inch on paper

16 ft in real life = (16/3) inches on paper

New width of the blueprint = (16/3) inches = 5.333 inches