Final answer:
The height of the speed limit sign is 6 feet, determined by using the proportionality of similar triangles created by the objects and their corresponding shadows.
Step-by-step explanation:
To determine the height of the speed limit sign, we use the concept of similar triangles. The relationship between the heights of objects and the lengths of their shadows will be proportional since the same sun casts both shadows. Specifically, the scarecrow's height to its shadow length is proportional to the sign's height to its shadow length.
Let's denote the height of the speed limit sign as 'h'. The scarecrow's height is 3 feet and its shadow is 4 feet long. The speed limit sign's shadow is 8 feet long. So the proportion is:
Scarecrow's height / Scarecrow's shadow = Sign's height / Sign's shadow
3 ft / 4 ft = h / 8 ft
To solve for 'h', we cross-multiply and divide:
(3 ft × 8 ft) / 4 ft = h
24 ft^2 / 4 ft = h
6 ft = h
Therefore, the height of the speed limit sign is 6 feet.