Cara is five feet tall and casts a shadow of eight feet long. At the same time, a building casts a shadow 32 feet long. What is the height of the building?
20
Cross multiply and solve for x.
5/8 = x/32
To find the height of the building, we can use the concept of proportions.
Let's assume the height of the building is "h" feet. According to the given information, Cara's height is 5 feet, and her shadow is 8 feet long. The building's shadow is 32 feet long.
We can set up a proportion using the lengths of the shadows and the heights:
Cara's height / Cara's shadow = Building's height / Building's shadow
Using the values we have:
5 feet / 8 feet = h feet / 32 feet
To find "h," we can cross-multiply and solve for "h":
5 feet * 32 feet = 8 feet * h feet
160 feet = 8h
To isolate "h," we divide both sides by 8:
160 feet / 8 = 8h / 8
20 feet = h
Therefore, the height of the building is 20 feet.
To find the height of the building, we can use proportions. Let's set up the proportion:
Height of Cara / Length of Cara's shadow = Height of the building / Length of the building's shadow
Height of Cara = 5 feet
Length of Cara's shadow = 8 feet
Length of the building's shadow = 32 feet
Let's substitute these values into our proportion:
5 feet / 8 feet = Height of the building / 32 feet
To solve for the height of the building, we can cross-multiply and then divide:
(5 feet) x (32 feet) = 8 feet x Height of the building
160 feet = 8 feet x Height of the building
Divide both sides of the equation by 8 feet:
160 feet / 8 feet = Height of the building
The height of the building is 20 feet.