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

223
2 Start Fraction 2 over 3 End Fraction

112
1 Start Fraction 1 over 2 End Fraction

−112
negative 1 Start Fraction 1 over 2 End Fraction

23

1 answer

To find the scale factor used to create the second television screen from the first, we need to compare the dimensions of the two screens.

The first television screen has the dimensions of 16 inches (width) by 9 inches (height). The second television screen has dimensions of 24 inches (width) by 13.5 inches (height).

To find the scale factor for the width: \[ \text{Width Scale Factor} = \frac{\text{Width of second television}}{\text{Width of first television}} = \frac{24}{16} = \frac{24 \div 8}{16 \div 8} = \frac{3}{2} \]

To find the scale factor for the height: \[ \text{Height Scale Factor} = \frac{\text{Height of second television}}{\text{Height of first television}} = \frac{13.5}{9} = \frac{13.5 \div 4.5}{9 \div 4.5} = \frac{3}{2} \]

Both the width and height scale factors are the same, \( \frac{3}{2} \).

Thus, the scale factor used to create the second television screen is \( \frac{3}{2} \).

The correct answer is: 2 Start Fraction 2 over 3 End Fraction.