Question

How does the area of the scale drawing where 1 centimeter represents 10 miles compare to the area of a the drawing where 1 centimeter represents 30 miles? Area if 1 cm= 10 mi: square miles Area if 1 cm = 30 mi: square miles The area would be times as great.

Answer 1

• 100 square miles
• 900 square miles
• 9 times as great

Explanation:

It seems rather obvious that ...

(1 cm)^2 ⇒ (10 mi)^2 = 100 mi^2 . . . on the first drawing

(1 cm)^2 ⇒ (30 mi)^2 = 900 mi^2 . . . on the second drawing

The area on the second drawing is 900/100 = 9 times as great.

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These are the areas represented by 1 square cm on the scale drawing. If the drawing is larger, then the represented area is correspondingly larger. The ratio of represented areas is still 9 times for drawings of the same size.