At a certain time of day, a pole, 5 meters tall, casts a 3 meter shadow. The shadow of the building beside the pole is 18 meters long. How tall is the building?
How long will the shadow of a 45 meter building be?
Use proportions to solve these problems.
5/3 = x/18
5/3 = 45/x
5/3 = x/18
5/3 = 45/x
Solve for x.
To find the height of the building beside the pole, we can set up a proportion using the height of the pole, the length of its shadow, and the length of the building's shadow.
Let's call the height of the building "x":
5 meters (pole height) : 3 meters (pole shadow) = x meters (building height) : 18 meters (building shadow)
To solve this proportion, we can use the property of cross-multiplication:
5 meters * 18 meters = 3 meters * x meters
90 meters = 3x
Next, we can divide both sides of the equation by 3 to isolate "x":
90 meters / 3 = 3x / 3
30 meters = x
Therefore, the height of the building beside the pole is 30 meters.
To find the length of the shadow of a 45 meter building, we can again set up a proportion using the height of the pole and the length of its shadow.
Let's call the length of the building's shadow "y":
5 meters (pole height) : 3 meters (pole shadow) = 45 meters (building height) : y meters (building shadow)
Using cross-multiplication again:
5 meters * y meters = 3 meters * 45 meters
5y = 135
Dividing both sides by 5:
5y / 5 = 135 / 5
y = 27
Therefore, the shadow of a 45 meter building will be 27 meters long.