Problem 2 · 2011 AMC 8
Easy
Geometry & Measurement
area-comparison
Karl's rectangular vegetable garden is 20 feet by 45 feet, and Makenna's is 25 feet by 40 feet. Which of the following statements are true?
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Answer: E — Makenna's garden is larger by 100 square feet.
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Hint 1 of 2
Don't compare the shapes — compare their areas. Area of a rectangle is length × width, so find both and subtract.
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Hint 2 of 2
Notice both gardens have the same half-perimeter (20+45 = 25+40 = 65). For a fixed perimeter, the rectangle whose sides are closer together holds more area — that hints Makenna (25 by 40) wins before you even multiply.
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Approach: multiply each area, then subtract
- Karl: 20 × 45 = 900 sq ft.
- Makenna: 25 × 40 = 1000 sq ft.
- Difference: 1000 − 900 = 100 ⇒ Makenna's is larger by 100 sq ft.
- Worth keeping: with the same perimeter, the "rounder" (squarer) rectangle always has more area — 25 by 40 is closer to a square than 20 by 45, so it had to be the bigger one.
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