Bobby draws an art work measuring 2.25 inches by 2 inches he makes a copy of the artwork enlarging it so that its dimensions are now 3.15 inches 2.8 inches. What scale factor did he use to create the copy of the original artwork? As a decimal

1 answer

To find the scale factor used by Bobby to enlarge his artwork, we can compare the lengths of corresponding sides of the original artwork and the enlarged copy.

The original artwork's dimensions are:

  • Width: 2.25 inches
  • Height: 2 inches

The dimensions of the enlarged artwork are:

  • Width: 3.15 inches
  • Height: 2.8 inches

We can calculate the scale factor for both the width and the height.

  1. Calculating the scale factor for the width: \[ \text{Scale Factor (Width)} = \frac{\text{Enlarged Width}}{\text{Original Width}} = \frac{3.15}{2.25} \]

    Performing the division: \[ \frac{3.15}{2.25} = 1.4 \]

  2. Calculating the scale factor for the height: \[ \text{Scale Factor (Height)} = \frac{\text{Enlarged Height}}{\text{Original Height}} = \frac{2.8}{2} \]

    Performing the division: \[ \frac{2.8}{2} = 1.4 \]

Since both the width and the height scale factors are the same, we can conclude that the scale factor for the enlargement is 1.4.

Thus, the scale factor Bobby used to enlarge his artwork is \(\boxed{1.4}\).