In the diagram, a building casts a 20-ft shadow and a flagpole casts a 7-ft shadow. If the flagpole is 12 ft tall, how high is the building? Round to the nearest tenth.

12/7 = x/20

7x = 240
x = 34.3 feet

To find the height of the building, we can use similar triangles. When two triangles are similar, the ratio of the lengths of their corresponding sides is equal.

Let's label the height of the building as "x."

According to the given information, the flagpole is 12 ft tall and casts a 7-ft shadow. Therefore, the ratio of the height of the flagpole to its shadow is 12/7.

Similarly, the building casts a 20-ft shadow. So the ratio of the height of the building to its shadow is x/20.

Since the two triangles (flagpole with its shadow and the building with its shadow) are similar, we can set up the following proportion:

12/7 = x/20

To solve for x, we can cross-multiply and then divide:

12 * 20 = 7 * x
240 = 7x
x = 240/7 ≈ 34.3

Therefore, the approximate height of the building is 34.3 ft.

To find the height of the building, we can set up a proportion using the similar triangles formed by the building and flagpole shadows.

Let's denote the height of the building as "x".

According to the given information:
Height of flagpole/Length of flagpole shadow = Height of building/Length of building shadow

Plugging in the values:
12 ft/7 ft = x/20 ft

To solve for x, we can cross-multiply and solve the equation:
7x = 12 * 20
7x = 240

Divide both sides of the equation by 7:
x = 240/7
x ≈ 34.3

Therefore, the height of the building is approximately 34.3 feet.