bilte Many drew a picture on a rectangular piece of paper that was 6 inches wide and 9 inches high. a. Write the aspeet ratio, and simplify it to lowest terms. b. If this picture were enlarged to be 20 inches wide, how high would it be? Ise equivalent ratios.

Let's solve each part of the problem step by step. --- **a. Write the aspect ratio and simplify it to lowest terms.** * **Aspect Ratio:** The aspect ratio is the ratio of the width to the height of the picture. \[ \text{Aspect Ratio} = \text{Width} : \text{Height} = 6\ \text{inches} : 9\ \text{inches} \] * **Simplifying the Aspect Ratio:** To simplify the ratio, divide both numbers by their greatest common divisor (GCD). The GCD of 6 and 9 is 3. \[ \frac{6}{3} : \frac{9}{3} = 2 : 3 \] **Simplified Aspect Ratio:** \(2 : 3\) --- **b. If the picture were enlarged to be 20 inches wide, how high would it be? Use equivalent ratios.** * **Original Dimensions:** - Width (\(W_1\)): 6 inches - Height (\(H_1\)): 9 inches * **Enlarged Dimensions:** - Width (\(W_2\)): 20 inches - Height (\(H_2\)): ? * **Setting Up the Proportion:** Since the aspect ratio remains the same when enlarging, we can set up the following proportion: \[ \frac{W_1}{H_1} = \frac{W_2}{H_2} \] Plugging in the known values: \[ \frac{6}{9} = \frac{20}{H_2} \] * **Solving for \(H_2\):** Cross-multiply to solve for \(H_2\): \[ 6 \times H_2 = 9 \times 20 \] \[ 6H_2 = 180 \] \[ H_2 = \frac{180}{6} = 30 \] **Height of Enlarged Picture:** \(30\) inches --- **Final Answers:** a. The aspect ratio is \(6 : 9\), which simplifies to \(2 : 3\). b. If the width is enlarged to \(20\) inches, the height would be \(30\) inches.