Question

A television has a screen that measures 16 inches by 9 inches. A second television has a screen measuring 24 inches by 13.5 inches. What scale factor was used to create the second television

Answer 1

To find the scale factor between the two televisions, we can compare their dimensions.

1. **Dimensions of the first television:**
- Width: 16 inches
- Height: 9 inches

2. **Dimensions of the second television:**
- Width: 24 inches
- Height: 13.5 inches

To find the scale factor, we can divide the dimensions of the second television by the corresponding dimensions of the first television:

- Scale factor for the width:
\[
\text{Scale factor (width)} = \frac{\text{Width of second television}}{\text{Width of first television}} = \frac{24}{16} = \frac{3}{2} = 1.5
\]

- Scale factor for the height:
\[
\text{Scale factor (height)} = \frac{\text{Height of second television}}{\text{Height of first television}} = \frac{13.5}{9} = \frac{3}{2} = 1.5
\]

Since both scale factors for width and height are equal, we can conclude the overall scale factor is:
\[
\text{Scale factor} = 1.5
\]

Therefore, the scale factor used to create the second television is **1.5**.