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Question
Find all the possible dimensions (in natural numbers) of a rectangle with a perimeter 36 cm and find their areas.
Solution
Perimeter of the rectangle = 36 cm
⇒ 2(Length + Breadth) = 36 cm
⇒ Length + Breadth = `36/2` cm = 18 cm
∴ The possible dimensions of the rectangle and their areas as follows:
| Dimensions | Area |
| 1 cm × 17 cm | 17 cm2 |
| 2 cm × 16 cm | 32 cm2 |
| 3 cm × 15 cm | 45 cm2 |
| 4 cm × 14 cm | 56 cm2 |
| 5 cm × 13 cm | 65 cm2 |
| 6 cm × 12 cm | 72 cm2 |
| 7 cm × 11 cm | 77 cm2 |
| 8 cm × 10 cm | 80 cm2 |
| 9 cm × 9 cm | 81 cm2 |
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