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 determine the height of the building, we can set up a proportion using the information given:
The height of the building / length of the building's shadow = height of the painter / length of the painter's shadow.
Let's assign variables to the given information:
Height of building = x
Length of building's shadow = 18 ft
Height of painter = 6 ft
Length of painter's shadow = 3 ft
Using the proportion, we can set up the equation as follows:
x/18 = 6/3
To solve for x, we can cross-multiply:
3x = 18 * 6
3x = 108
Now, divide both sides of the equation by 3 to solve for x:
x = 108/3
x = 36
Therefore, the height of the building is 36 ft.
To find the height of the building, we can use a proportion based on the lengths of the shadows. Here's how to solve it step by step:
Step 1: Understand the given information.
- Height of the painter (H_painter): 6 ft
- Length of the painter's shadow (L_painter_shadow): 3 ft
- Length of the building's shadow (L_building_shadow): 18 ft
Step 2: Set up a proportion.
Based on the information given, we can set up a proportion relating the lengths of the shadows to the heights of the objects:
L_building_shadow / L_painter_shadow = Height_building / H_painter
Step 3: Substitute the values into the proportion.
Plugging in the given values, we get:
18 ft / 3 ft = Height_building / 6 ft
Step 4: Solve for Height_building.
To solve for Height_building, we can cross-multiply and then solve for the unknown:
18 ft * 6 ft = 3 ft * Height_building
108 ft = 3 ft * Height_building
Step 5: Divide both sides by 3 ft to isolate Height_building.
Divide both sides by 3 ft:
108 ft / 3 ft = Height_building
36 ft = Height_building
Step 6: Find the answer.
The height of the building is 36 ft.
So, the building is 36 ft tall.