1. My Rectangle Select the rectangle that you will be investigating and measure the length and width to the nearest 5 cm . The length will be the bigger number and the width will be the smaller number. What is your rectangle? TV Screen My rectangle's real length is $$ 120 \quad \mathrm{~cm} $$, and its real width is 70 cm . 2. My Scale Measurements a) This rectangle will be too big to draw it full size, so we will use a smaller "scale" version by dividing each measurement (length and width) by the same large number. Choose your large number to make the rectangle's length between 5 cm and 10 cm . This large number must be two digits with no zeros in it. For example, the number could be 57 but not 100 or not 70 . Use your calculator to help you choose your number. My large number is

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UpStudy AI · Accepted Answer

1. We are given the real dimensions of the TV screen as  
   $$
   \text{Length} = 120\,\text{cm} \quad \text{and} \quad \text{Width} = 70\,\text{cm}.
   $$

2. We need to choose a two‐digit number (with no zeros) to scale down the drawing so that the scaled length is between $$5\,\text{cm}$$ and $$10\,\text{cm}$$.

Let the large number be $$\ell$$. The scaled length is  
   $$
   \frac{120}{\ell}.
   $$

We require  
   $$
   5 \le \frac{120}{\ell} \le 10.
   $$

3. To find the allowable values for $$\ell$$, solve the inequalities step by step:

- For the upper bound:
     $$
     \frac{120}{\ell} \le 10 \quad \Rightarrow \quad \ell \ge \frac{120}{10} = 12.
     $$
     
   - For the lower bound:
     $$
     \frac{120}{\ell} \ge 5 \quad \Rightarrow \quad \ell \le \frac{120}{5} = 24.
     $$

So, $$\ell$$ must satisfy  
   $$
   12 \le \ell \le 24.
   $$

4. In addition, the number must be a two-digit number with no zeros. This means valid selections for $$\ell$$ include any two-digit number between 12 and 24 (excluding numbers like 20 since it has a zero).

5. One acceptable choice is $$\ell = 17$$. Then the scaled dimensions are:
   
   - Scaled length:  
     $$
     \frac{120}{17} \approx 7.06\,\text{cm},
     $$
     which is between $$5\,\text{cm}$$ and $$10\,\text{cm}$$.
     
   - Scaled width:  
     $$
     \frac{70}{17} \approx 4.12\,\text{cm}.
     $$

Thus, one valid answer is:  
$$
\boxed{17}
$$
A suitable large number to scale the TV screen is **17**.

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