Problem 4 · 2021 Math Kangaroo
Medium
Geometry & Measurement
area
Six rectangles are arranged as shown. The top left-hand rectangle has height 6 cm. The numbers within the rectangles indicate their areas in cm². What is the height of the bottom right-hand rectangle?
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Answer: B — 5 cm
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Hint 1 of 2
The top-left rectangle has height 6 and area 18, so its width is 3 — then chain that through neighbours that share a side.
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Hint 2 of 2
Each shared edge passes a known length along; follow the chain until you reach the bottom-right rectangle's width, then divide its area by that width.
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Approach: propagate shared side lengths through the areas
- Top-left has height 6 and area 18, so its width is 18÷6 = 3.
- Bottom-left shares that width 3 and has area 12, so its height is 12÷3 = 4; the bottom-middle rectangle shares this height 4 and has area 16, so its width is 16÷4 = 4.
- Top-middle shares width 4 and area 32, so its height is 32÷4 = 8; top-right shares that height 8 and area 48, so its width is 48÷8 = 6.
- The bottom-right rectangle shares this width 6 and has area 30, so its height is 30÷6 = 5 cm, choice (B).
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