Brandon wants to reduce a figure that is 9 inches tall and 16 inches wide so that it will fit on a 9-inch-by-12-inch piece of paper.

Question

If he reduces the figure proportionally, what is the maximum size the reduced figure could measure?

Answer 1

Figure: 9 in × 16 in 

Paper: 9 in × 12 in

 

The figure needs to be reduced by multiple < 1 to make it the same height to width ratio as the paper. The height of the figure and paper is the same, 9 in so it fits vertically on the paper. The width needs to be reduced to minimum 12 in.

 

16x = 12

x = 12/16

x = 3/4

 

The width needs to be reduced to 3/4 it's normal size to just barely fit on the paper. This would be the maximum size it can be. To keep the scale of the figure proportional the height would also need to be reduced to 3/4 it's normal size.

 

Height:

9 in * (3/4) = 6.75 in

Width:

16 in * (3/4) = 12 in

 

New scale

 

6.75 in × 12 in