ess in Mathematics - 7th grade \( > \) FF. 5 Similar figures and indirect measurement 8 V , Clara found that a crane that is 30 yards tall casts a shadow 16 yards long. Then Clara noticed a nearby windmill that is 60 yards tall. How long is the windmill's shadow? Write your answer as a whole number or a decimal. Do not round.

To solve this problem, we can use the concept of similar figures, which states that the ratios of corresponding lengths in similar figures are equal. Here, Clara's crane and the windmill form two similar triangles with their heights and shadow lengths. We can set up a proportion using the heights and shadow lengths: \[ \frac{\text{Height of Crane}}{\text{Shadow of Crane}} = \frac{\text{Height of Windmill}}{\text{Shadow of Windmill}} \] Substituting in the known values, we get: \[ \frac{30 \text{ yards}}{16 \text{ yards}} = \frac{60 \text{ yards}}{x} \] Now we can cross-multiply: \[ 30x = 60 \times 16 \] \[ 30x = 960 \] Dividing both sides by 30 gives: \[ x = \frac{960}{30} = 32 \] So, the shadow of the windmill is 32 yards long. If you found this math magic fascinating, you might enjoy exploring the broader world of ratios and proportions! These concepts underpin so many real-world applications, from architecture to culinary arts, where precise measurements are essential. Additionally, it's always helpful to double-check your work—especially with ratios! A common mistake is to misplace a number or incorrectly set up the proportion. Slow down, take a breath, and before you solve, ensure the relationships are laid out correctly for accurate answers.