Sarah wants to build a model of the Golden Gate Bridge for a school project. She decides that her scale model needs to be 1/20th the size of the real bridge. When she looked online, Sarah found that the base of the bridge is 4,200 ft long and 90 ft wide. If she uses a scale of inches to feet, what are the dimensions of her model? What is the scale factor?
the real scale model would have a base of 4200/20 ft or 210 ft
by 90/20 or 4.5 ft
She wants to reduce this even further so that 1 inch represents 1 foot
so her model should have a length of 210/12 inches or 17.5 inches
and a width of 4.5/12 or .375 inches, the same as 3/8 of an inch
so 17.5 by 3/8 inches
To find the dimensions of the model, we need to apply the scale of 1/20th to the real dimensions of the bridge.
First, let's convert the units from feet to inches for easier calculations. Since there are 12 inches in a foot, we multiply the dimensions by 12.
- The length of the real bridge is 4,200 ft * 12 inches/foot = 50,400 inches.
- The width of the real bridge is 90 ft * 12 inches/foot = 1,080 inches.
Next, we apply the scale factor of 1/20th to the real dimensions to find the dimensions of the model:
- Length of the model = 50,400 inches * 1/20 = 2,520 inches.
- Width of the model = 1,080 inches * 1/20 = 54 inches.
Therefore, the dimensions of Sarah's model Golden Gate Bridge are 2,520 inches long and 54 inches wide.
The scale factor is calculated by dividing the real dimensions by the model dimensions:
- Scale factor for length = 50,400 inches / 2,520 inches = 20.
- Scale factor for width = 1,080 inches / 54 inches = 20.
So, the scale factor is 20, indicating that every inch on the model represents 20 inches on the real bridge.