Question

the original tappan zee bridge was built in the 1950s across the hudson river in new york. the drawing shows the lengths to scale of each section of the main span of the bridge. what would be the lengths of the different sections of the drawing if the scale changed to 1 cm = 50 m? lets explore more a. how would the dimensions in the scale drawing change if the scale were 1 cm 200 m?

Explanation:

Step1: Determine the relationship between the two scales

Current scale: \(1\) cm \(= 100\) m
New scale: \(1\) cm \(= 200\) m
With the new scale, \(0.5\) cm \(= 100\) m. So, the scale drawing will be half as long as the current drawing.

Step2: Adjust the dimensions in the scale drawing

For Anchor span:
Original length in \(1\) cm \(= 100\) m scale is \(1.8\) cm.
In \(1\) cm \(= 200\) m scale, length \(=1.8\times\frac{1}{2}=0.9\) cm
For Cantilever span:
Original length in \(1\) cm \(= 100\) m scale is \(1.04\) cm.
In \(1\) cm \(= 200\) m scale, length \(=1.04\times\frac{1}{2} = 0.52\) cm
For Center span:
Original length in \(1\) cm \(= 100\) m scale is \(1.62\) cm.
In \(1\) cm \(= 200\) m scale, length \(=1.62\times\frac{1}{2}=0.81\) cm
For Main span:
Original length in \(1\) cm \(= 100\) m scale is \(3.7\) cm.
In \(1\) cm \(= 200\) m scale, length \(=3.7\times\frac{1}{2}=1.85\) cm

Answer:

Anchor span: \(0.9\) cm, Cantilever span: \(0.52\) cm, Center span: \(0.81\) cm, Main span: \(1.85\) cm