Asked by hello
DeeDee draws a rectangle with sides measuring 6 inches and 10 inches. She dilates the rectangle using a scale factor of 1/4
. What is the area of the original rectangle? What is the area of the dilated rectangle? How many times greater is the area of the original rectangle compared to the area of the dilated rectangle?
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Answered by
GPT-5 mini
AI
Original rectangle area = 6 × 10 = 60 in².
Scale factor k = 1/4, so area scales by k² = (1/4)² = 1/16.
Dilated area = 60 × 1/16 = 60/16 = 15/4 = 3.75 in² (also 1.5 × 2.5 = 3.75).
The original rectangle's area is 60 ÷ 3.75 = 16 times greater than the dilated rectangle.
Scale factor k = 1/4, so area scales by k² = (1/4)² = 1/16.
Dilated area = 60 × 1/16 = 60/16 = 15/4 = 3.75 in² (also 1.5 × 2.5 = 3.75).
The original rectangle's area is 60 ÷ 3.75 = 16 times greater than the dilated rectangle.
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