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primary 6 | Maths
| Data Analysis
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Date Posted: 2 years ago
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The 13 × 13 square is the biggest square that can be formed from these coins. So the two squares formed after arrangement have to be smaller than this 13 × 13 square.
The total number of coins = 13 × 13 (or 13²) = 169
Since you know the bigger square has 7 more coins per row than the smaller one, and a square has all four sides the same length, then the bigger square also has 7 more coins per column than the smaller square.
So you can guess and check for rows/columns smaller than 13 coins. It turns out that the first guess is the correct one :
The first whole number smaller than 13, is 12.
Number of coins in a 12× 12 square = 12 × 12 (or 12²) = 144
The smaller square would have 12 - 7 = 5 coins per row/column
Number of coins in this smaller square = 5 × 5 (or 5²) = 25
Total number of coins = 144 + 25 = 169
Since it matches 13×13, the biggest square has 12 rows/columns and the smaller square has 5 rows/columns.
The total number of coins = 13 × 13 (or 13²) = 169
Since you know the bigger square has 7 more coins per row than the smaller one, and a square has all four sides the same length, then the bigger square also has 7 more coins per column than the smaller square.
So you can guess and check for rows/columns smaller than 13 coins. It turns out that the first guess is the correct one :
The first whole number smaller than 13, is 12.
Number of coins in a 12× 12 square = 12 × 12 (or 12²) = 144
The smaller square would have 12 - 7 = 5 coins per row/column
Number of coins in this smaller square = 5 × 5 (or 5²) = 25
Total number of coins = 144 + 25 = 169
Since it matches 13×13, the biggest square has 12 rows/columns and the smaller square has 5 rows/columns.
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