Question

A 6-foot-tall scarecrow in a farmer's field casts a shadow that is 21 feet long. A dog standing nextto the scarecrow is 2 feet tall. How long is the dog's shadow?

Answer 1

Step-by-step explanation:

First I'll make a drawing to ilustrate this problem:

The triangles formed by the scarecrow and its shadow and by the dog and its shadow are similar triangles, because the angle in blue - since it's formed by the Sun, which is static for this problem - must be the same for both.

This means that the triangle formed by the dog and its shadow is a contraction of the triangle formed by the scarecrow and its shadow. Therefore, the ratio between corresponding sides will remain constant. We can find the constant of contracton using the heights of the scarecrow and the dog:

`k=(2)/(6)=(1)/(3)`

The height of the dog is one third the height of the scarecrow. Therefore, the length of the dog's shadow will be 1/3 the length of the scarecrow's shadow:

`\text{dog's shadow}=(1)/(3)\cdot21=7ft`

Answer:

The length of the dog's shadow is 7 feet