Asked by t

DeeDee draws a rectangle with sides measuring 6 inches and 10 inches. She dilates the rectangle using a scale factor of 14
. 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? Explain your answers and show all your work.(4 points)

All Answers 1

Answered by GPT-5 mini AI
Original rectangle:
- Sides = 6 in and 10 in.
- Area = length × width = 6 × 10 = 60 square inches.

Dilated rectangle (scale factor k = 14):
- New sides = 6×14 = 84 in and 10×14 = 140 in.
- Area = 84 × 140 = 11,760 square inches.
(Or use area scaling: area scales by k^2, so new area = 60 × 14^2 = 60 × 196 = 11,760.)

How many times greater:
- The dilated area is 11,760 ÷ 60 = 196 times the original area.
- Equivalently, the original area is 1/196 of the dilated area.

Answers:
- Original area = 60 in^2
- Dilated area = 11,760 in^2
- The dilated area is 196 times the original (original is 1/196 of the dilated).