A painter needs to know the height of a building to estimate the amount of
paint needed for the front side. When the building cast an 18 ft shadow,
the 6 ft tall painter casts a 3 ft long shadow. How tall is the building?
36ft
To find the height of the building, we can use a proportion: the height of the building's shadow is proportional to the height of the building itself.
Let's define the variables:
- Height of the building = H
- Length of the building's shadow = S
- Height of the painter = P
- Length of the painter's shadow = p
Given:
- Length of the building's shadow (S) = 18 ft
- Length of the painter's shadow (p) = 3 ft
- Height of the painter (P) = 6 ft
Using the proportion, we can set up the following equation:
(Height of the building) / (Length of the building's shadow) = (Height of the painter) / (Length of the painter's shadow)
H / S = P / p
Now, let's plug in the given values and solve for the height of the building:
H / 18 = 6 / 3
Cross-multiplying, we have:
H * 3 = 18 * 6
H * 3 = 108
Dividing both sides by 3:
H = 108 / 3
H = 36
Therefore, the height of the building is 36 ft.
To find the height of the building, we can use the concept of similar triangles.
First, let's set up the proportion:
(height of building) / (length of building's shadow) = (height of painter) / (length of painter's shadow)
Let's substitute the given values into the proportion:
(height of building) / 18 ft = 6 ft / 3 ft
Now, we can cross-multiply and solve for the height of the building:
(height of building) * 3 ft = 6 ft * 18 ft
(height of building) * 3 ft = 108 ft
To isolate the height of the building, divide both sides of the equation by 3 ft:
height of building = 108 ft / 3 ft
height of building = 36 ft
Therefore, the height of the building is 36 ft.