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| Math Central | Quandaries & Queries |
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Question from Lisa, a student: Hi! Joe wants to enlarge a picture so that its area is doubled. |
Hi Lisa,
Did you experiment?
Suppose this is a small rectangular picture, 30 cm by 15 cm. Its area is then 30 × 15 = 450 square centimeters.
- If you double the side lengths to 60 cm by 30 cm what happens to the area? By what factor does it increase? Can you see why from the formula for the area of a rectangle?
- If you triple the side lengths to 90 cm by 45 cm what happens to the area? By what factor does it increase? Can you see why from the formula for the area of a rectangle?
- By what scale factor do you need to multiply the side lengths to have an area factor of 2?
Try the same experiment with a circle of radius 20 cm.
Penny
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