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)

Question

Responses

−112
negative 1 Start Fraction 1 over 2 End Fraction

223
2 Start Fraction 2 over 3 End Fraction

112
1 Start Fraction 1 over 2 End Fraction

23

Answer 1

To find the scale factor between the two television screens, we can compare the dimensions of the first television screen to the dimensions of the second television screen.

The dimensions of the first television are 16 inches (width) and 9 inches (height). The dimensions of the second television are 24 inches (width) and 13.5 inches (height).

To find the scale factor for the width:

\[ \text{Scale Factor (Width)} = \frac{\text{Width of second television}}{\text{Width of first television}} = \frac{24}{16} = \frac{3}{2} \]

To find the scale factor for the height:

\[ \text{Scale Factor (Height)} = \frac{\text{Height of second television}}{\text{Height of first television}} = \frac{13.5}{9} = \frac{3}{2} \]

Since both scales are equal, the scale factor from the first television to the second television is \( \frac{3}{2} \) or 1.5.

Thus, the correct response is \( \frac{3}{2} \).