🇺🇸 AMC 8 ⇄ switch contest
1995 AJHSME

Problem 6

Problem 6 · 1995 AJHSME Medium
Geometry & Measurement perimeter-side
Figure for AJHSME 1995 Problem 6
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Answer: C — 36.
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Hint 1 of 2
Perimeter and side of a square are locked together: side = perimeter ÷ 4. So a perimeter instantly tells you a side — work in sides, not perimeters.
Still stuck? Show hint 2 →
Hint 2 of 2
Look at how the squares stack in the picture: the big square's left edge is exactly as tall as the two smaller squares stacked. So its side is the SUM of the two small sides.
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Approach: convert perimeters to sides, read the side relationship from the picture
  1. First turn each perimeter into a side (a square's side is perimeter ÷ 4, since all four sides match): square I has side 12 ÷ 4 = 3, square II has side 24 ÷ 4 = 6.
  2. Now read the figure: the big square III runs alongside squares I and II stacked together, so its side equals 3 + 6 = 9.
  3. Perimeter of III = 4 × 9 = 36.
  4. Why this transfers: for squares, perimeter, side, and area are all instantly convertible (÷4, then square). The real work is always reading how the sides line up in the picture.
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