Question

A 14 ft tall fence casts a 40 ft shadow. If a cardboard box casts a 70 ft shadow, how tall is it?

a) 25 ft
b) 49 ft
c) 140 ft
d) 70 ft

Answer 1

The height of the cardboard box is found through the proportion of similar triangles, comparing the height and shadow length of the fence to those of the cardboard box. The height of the cardboard box is approximately 25 feet.

Step-by-step explanation:

To determine the height of the cardboard box based on its shadow and comparing it to the known height and shadow length of a fence, we can apply the concept of similar triangles. Here, the ratio of the height of the fence to its shadow length should be the same as the ratio of the height of the box to its shadow length because the sun's rays provide the same angle of elevation for both objects.

Let's set up a proportion using the information given:

• Fence height to fence shadow = Box height to box shadow
• 14 ft / 40 ft = Box height / 70 ft

To find the box height, cross-multiply and solve for the box height:

(14 ft × 70 ft) / 40 ft = Box height

This gives us:

• 980 ft2 / 40 ft = 24.5 ft, which we can round up to the nearest foot if required.

So, the height of the cardboard box is approximately 25 feet, which corresponds to option (a).