If a building casts a 20 ft shadow and a flagpole casts a 7 ft shadow and the flagpole is 12 ft tall, how high is the building?

One way to solve this is with a proportion. Cross multiply and solve for x.

x/20 = 12/7

34.3

To determine the height of the building, we can use the concept of similar triangles.

Similar triangles have proportional sides that maintain the same ratio. In this case, we can form two similar triangles: one with the building and its shadow, and the other with the flagpole and its shadow.

Let's label the height of the flagpole as "x" and the height of the building as "h". We also know that the length of the flagpole's shadow is 7 ft and the length of the building's shadow is 20 ft.

Using the concept of similar triangles, we can set up the following proportion:

h / x = 20 / 7

Now, let's solve for "h":

h = (20 / 7) * x

Since we know the height of the flagpole is 12 ft, we can substitute this value into the equation:

h = (20 / 7) * 12

h = 34.29 ft

Therefore, the height of the building is approximately 34.29 ft.