To determine the dimensions of the brand name television, we start with the dimensions of the generic television and use the given size ratio between the generic and the brand name television.
1. The dimensions of the generic television are given as:
- Length: 12 inches
- Width: 24 inches
2. The size of the generic television is stated to be [tex]\(\frac{2}{3}\)[/tex] the size of the brand name television. This implies that:
- Generic Length = [tex]\(\frac{2}{3}\)[/tex] Brand Length
- Generic Width = [tex]\(\frac{2}{3}\)[/tex] Brand Width
3. To find the dimensions of the brand name television, we need to solve for Brand Length and Brand Width.
4. Starting with the length:
- Generic Length = [tex]\(\frac{2}{3}\)[/tex] Brand Length
- 12 = [tex]\(\frac{2}{3}\)[/tex] Brand Length
- To find the Brand Length, we can rearrange the equation:
[tex]\[
\text{Brand Length} = \frac{12}{\frac{2}{3}} = 12 \times \frac{3}{2} = 18 \text{ inches}
\][/tex]
5. Next, for the width:
- Generic Width = [tex]\(\frac{2}{3}\)[/tex] Brand Width
- 24 = [tex]\(\frac{2}{3}\)[/tex] Brand Width
- To find the Brand Width, we can rearrange the equation:
[tex]\[
\text{Brand Width} = \frac{24}{\frac{2}{3}} = 24 \times \frac{3}{2} = 36 \text{ inches}
\][/tex]
Therefore, the dimensions of the brand name television are:
- Length: 18 inches
- Width: 36 inches
So, the correct answer is:
[tex]\[
\boxed{18 \text{ inches by } 36 \text{ inches}}
\][/tex]
