Problem 15 · 1990 AJHSME
Hard
Geometry & Measurement
perimetertetromino
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Answer: E — 50 cm.
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Hint 1 of 2
First turn the area into a length. Four equal squares share the 100 cm², so one square is 25 cm² — and 25 is a perfect square, which hands you the side instantly.
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Hint 2 of 2
For the perimeter, don't measure with a ruler — count how many square-sides lie on the *outside* of the S-shape. Inner edges where two squares touch are hidden and don't count.
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Approach: area → side, then count only the outer square-edges
- The four squares are identical and total 100 cm², so each is 25 cm². Since 5×5 = 25, each square has side 5 cm.
- Now trace the boundary of the S-shaped figure and count the side-lengths on the outside: there are 10 of them (the edges where two squares meet are interior and don't show).
- Perimeter = 10 × 5 = 50 cm.
- *Worth keeping:* for shapes built from equal squares, find the side from one square's area, then perimeter = (count of exposed square-edges) × side — you only ever count the *outside* edges.
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