#### Answer

42 inches wide.

#### Work Step by Step

The two images are like shapes as one image is the projection of the original drawing. Thus, we know that all of the sides are proportional, allowing us to set up the following equation: $27/4.5=x/7$, where x is the width of the projected image. We see that the variable only appears in the numerator of the fractions, so we know that the Multiplication Property of Equality will work well. We multiply both sides of the equation by 7 to obtain that x=42. Thus, the projected image will be 42 inches wide.