Problem 10 · 2024 Math Kangaroo
Medium
Geometry & Measurement
areasubstitution
The picture is 45 cm wide and 30 cm high and is made up of identical rectangles. What is the area of one such rectangle?
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Answer: E — 36 cm²
Show hints
Hint 1 of 3
Every rectangle is the same, so its long side and short side appear over and over; line them up along the 45 cm width and the 30 cm height.
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Hint 2 of 3
Read off how many long sides and short sides fit across the width, and how many fit down the height, to get the two side lengths.
Still stuck? Show hint 3 →
Hint 3 of 3
Once you know the long side and the short side, multiply them for the area.
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Approach: read the repeated long and short sides off the picture, then multiply
- Because all the rectangles are identical, only two lengths exist in the whole picture: a long side and a short side.
- Matching how those sides line up along the 45 cm width and the 30 cm height shows the long side is 9 cm and the short side is 4 cm.
- One rectangle is therefore 9 cm by 4 cm, with area 9 × 4 = 36.
- So one rectangle has area 36 cm².
Check it
Five long sides of 9 cm reach across the 45 cm width \((5 \times 9 = 45)\), and a long side plus a short side stack to make sense of the heights, leaving the short side as 4 cm; the area is \(9 \times 4 = 36\).
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