9. Two brothers are outside on a hot day. Timothy, who is 5 ft 6 in tall, casts a shadow that is 8 ft in length. If his brother, Jacob is 3 ft 6 in tall, how long of a shadow will Jacob cast?

To find the length of Jacob's shadow, we can use the concept of similar triangles. The ratio of the height of an object to the length of its shadow will be the same for both Timothy and Jacob. First, we need to convert their heights into inches for easier calculation: - Timothy's height: 5 ft 6 in = 5 * 12 + 6 = 60 + 6 = 66 inches - Jacob's height: 3 ft 6 in = 3 * 12 + 6 = 36 + 6 = 42 inches Now we can set up the proportion based on their heights and shadow lengths: \[ \frac{\text{Height of Timothy}}{\text{Shadow of Timothy}} = \frac{\text{Height of Jacob}}{\text{Shadow of Jacob}} \] Substituting the known values: \[ \frac{66}{8} = \frac{42}{x} \] Where \( x \) is the length of Jacob's shadow. Now we can cross-multiply to solve for \( x \): \[ 66x = 8 \times 42 \] Calculating the right side: \[ 66x = 336 \] Now, divide both sides by 66 to find \( x \): \[ x = \frac{336}{66} \approx 5.09 \] Thus, Jacob's shadow will be approximately 5.09 feet long.