Question

zoom in
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.
scale: 1 cm = 100 m
what would be the lengths of the different sections of the
drawing if the scale changed to 1 cm = 50 m?
math is... analyzing
what information do you know?
what information do you need?
step 1 determine the relationship
step 2 adjust the dimensions in the scale drawing.
between the two scales.
current scale: 1 cm : 100 m
new scale: 1 cm : 50 m
with the new scale, 1 cm = 50 m and
2 cm = 100 m. so, the scale drawing
will be twice as long as the current
drawing.
lets explore more
a. how would the dimensions in the scale drawing change if the scale were
1 cm : 200 m?
b. why might an architect want to change a scale for a model or drawing?

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, \(2\ cm = 200\ m\) and \(1\ cm = 100\ m\). So, the scale drawing will be half as long as the current drawing.

Step2: Adjust the dimensions in the scale drawing

• Anchor span: \(1.8\div2 = 0.9\ cm\)
• Cantilever span: \(1.04\div2 = 0.52\ cm\)
• Center span: \(1.62\div2 = 0.81\ cm\)
• Main span: \(3.7\div2 = 1.85\ cm\)

Answer:

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