A tall building casts a shadow of 20 meters. John, who is 1.5 meters tall, casts a shadow of 10 cm. how tall is the building?
h/20 = 1.5/0.1
150 cm /10 cm = x/2000 cm
cross multiply to get x
10x = (150)(2000)
divide by 10 to find answer in cm.
change to meters by dividing by 100.
To find the height of the building, we can use proportions.
Let's set up a proportion between the height of the building and the length of its shadow, as well as the height of John and the length of his shadow.
Height of building / Length of building's shadow = Height of John / Length of John's shadow
We know that the height of John is 1.5 meters and the length of his shadow is 10 cm.
Plugging in these values:
Height of building / 20 meters = 1.5 meters / 10 cm
To make the units consistent, we need to convert 10 cm to meters. Since 1 meter is equal to 100 centimeters, we divide 10 cm by 100:
1.5 meters / (10 cm / 100 cm) = Height of building / 20 meters
Simplifying the equation:
1.5 meters / 0.1 meters = Height of building / 20 meters
This gives us:
15 = Height of building / 20
To solve for the height of the building, we can cross multiply:
15 * 20 = Height of building
Height of building = 300 meters
Therefore, the height of the building is 300 meters.