A woman who is 6-ft tall casts a 4.5-foot shadow at the same time that a building casts a 75-foot shadow. What is the height of the building in feet?
set up a ratio
height/75 = 6/45 and solve for height
10
To find the height of the building, we can use similar triangles and set up a proportion. The height of the woman and the height of the building are proportional to their respective shadows.
Let's assign variables to the unknown quantities:
- Height of the woman = w
- Height of the building = b
- Length of the woman's shadow = s_w
- Length of the building's shadow = s_b
We are given:
w = 6 feet
s_w = 4.5 feet
s_b = 75 feet
Now we can set up the proportion:
w/s_w = b/s_b
Substituting the given values:
6/4.5 = b/75
To find the value of b, we can cross-multiply and solve for it:
6 × 75 = 4.5 × b
450 = 4.5b
To solve for b, divide both sides of the equation by 4.5:
b = 450/4.5
b = 100
Therefore, the height of the building is 100 feet.