A television has a rectangular 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 screen?(1 point) Responses −112 negative 1 Start Fraction 1 over 2 End Fraction 23 Start Fraction 2 over 3 End Fraction 223 2 Start Fraction 2 over 3 End Fraction 112 1 Start Fraction 1 over 2 End Fraction

1 answer

To find the scale factor used to create the second television screen from the first television screen, we can calculate the scale factor by comparing the dimensions of the two screens.

First, let's look at the dimensions of the first television screen:

  • Width: 16 inches
  • Height: 9 inches

Next, we look at the dimensions of the second television screen:

  • Width: 24 inches
  • Height: 13.5 inches

Now, we'll find the scale factors for both dimensions separately.

  1. For the width: \[ \text{Scale factor for width} = \frac{\text{Width of second TV}}{\text{Width of first TV}} = \frac{24}{16} = \frac{3}{2} \text{ or } 1.5 \]

  2. For the height: \[ \text{Scale factor for height} = \frac{\text{Height of second TV}}{\text{Height of first TV}} = \frac{13.5}{9} = \frac{3}{2} \text{ or } 1.5 \]

Since both the width and height have the same scale factor of \( \frac{3}{2} \), we conclude that the overall scale factor from the first television to the second television is:

\[ \text{Scale factor} = \frac{3}{2} \]

Thus, the correct response is:

\(\frac{3}{2}\).