Question

The bird house in your friend's yard casts a shadow that is 14 feet long. Your friend is 5 feet tall and casts a shadow that is 3.5 feet long. What is the height of the bird house?

Answer 1

Explanation:

that creates 2 similar triangles.

that means all angles are the same, and all side lengths of one triangle correlate to the corresponding side lengths of the other triangle by the same multiplication factor.

so,

3.5 × f = 14

f = 14/3.5 = 4

and now the range factor applies in the relation between the heights :

5 × 4 = 20 ft

the bird house is 20 ft high.

Answer 2

20 ft

Explanation:

The shadow of the bird house is 14/3.5 = 4 times the length of your friend's shadow. Consequently, we expect the height of the bird house to be 4 times the height of your friend:

4(5 ft) = 20 ft

The height of the bird house is 20 ft.