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

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: \[ \boxed{17} \]