Using the principle of similar triangles, the height of the cardboard box is found to be 24.5 ft by setting up a ratio of the tent's height to its shadow and the cardboard box's shadow to its unknown height.
The length of the shadow cast by an object is directly proportional to the height of the object when the sun's rays are at the same angle. To find the height of the cardboard box, we set up a ratio comparing the height and shadow length of the tent to the height and shadow length of the cardboard box.
The ratio for the tent is 14 ft (height) to 40 ft (shadow length). We need to find the height (h) of the cardboard box that has a 70 ft shadow:
14 ft / 40 ft = h / 70 ft
Cross-multiplying gives us:
14 ft × 70 ft = 40 ft × h
980 = 40h
Divide both sides by 40 to get h:
h = 980 / 40 = 24.5 ft
Therefore, the height of the cardboard box is 24.5 ft, which corresponds to option A.