Final answer:
To find the actual height of a house, given its miniature model height and scale, set up a proportion using the given scale and solve for the actual height. In this case, the proportion is 0.75 inch to 6 feet as 4 inches to x feet, which results in the actual height being 32 feet.
Step-by-step explanation:
To find the actual height of the house when a miniature house measures 4 inches tall using the scale of 0.75 inch : 6 feet, we need to set up a proportion. The scale tells us that 0.75 inch on the model represents 6 feet on the actual house. Therefore, the proportion will be:
- Scale: 0.75 inch / 6 feet
- Model Height: 4 inches / x feet
We can set this up as a fraction equation to solve for x:
0.75 inch / 6 feet = 4 inches / x feet
Now, we cross multiply and solve for x:
0.75x = 4 * 6
0.75x = 24
x = 24 / 0.75
x = 32 feet
Thus, the actual height of the house is 32 feet.