Final answer:
By setting up a proportion based on similar triangles, we find that a cardboard box casting a 6 ft shadow next to a 6 ft tall tent casting a 9 ft shadow is 4 ft tall.
Step-by-step explanation:
The question involves using similar triangles to find the height of an object based on its shadow length when compared to another object and its shadow. This type of problem is commonly found in geometry, a branch of mathematics. Given that a 6 ft tall tent casts a 9 ft shadow, and a cardboard box casts a shadow that is 6 ft long, we can use the ratio of the heights to the shadows to find the height of the cardboard box.
We set up a proportion:
Tent height / Tent shadow = Box height / Box shadow
6 ft / 9 ft = Box height / 6 ft
To find the height of the cardboard box, we cross-multiply and solve:
Box height = (6 ft × 6 ft) / 9 ft
Box height = 36 ft² / 9 ft
Box height = 4 ft
So, the cardboard box is 4 ft tall.