Problem 16 · 2021 Math Kangaroo
Medium
Geometry & Measurement
Algebra & Patterns
spatial-reasoning
Five squares are positioned as shown. The small square indicated has area 1. What is the value of h?
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Answer: C — 4 m
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Hint 1 of 2
The marked small square has area 1, so its side is 1; use it as the unit of length.
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Hint 2 of 2
Work along the staircase of squares to express h in those units.
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Approach: measure with the unit square
- The marked small square has area 1, so its side is 1; use that as the unit of length along the figure.
- Each larger square's side is set by stacking on the one beside it, so the side lengths grow by fixed steps measured in those units.
- The arrow h reaches across the top from the small square's structure to the far edge of the big right-hand square, and summing those side-steps gives h = 4 m.
- So the answer is C.
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