In a garden, there are 10 rows and 12 columns of mango trees. The distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden. The length of the garden is

### Concept & Strategy This question requires calculating physical dimensions based on a grid pattern. The "length" of a rectangular area refers to its longest side. Like linear fencepost problems, the number of gaps between trees in a row is one less than the number of trees. The total length equals the distance covered by the gaps plus the boundary margins. ### Step-by-Step Solution * **Given:** The grid has 10 rows and 12 columns. Gap between trees = 2 metres. Boundary margin = 1 metre on all sides. * First, establish which dimension represents the "length". The columns represent the horizontal dimension (spanning 12 trees), and rows represent the vertical dimension (spanning 10 trees). The side with 12 trees will be the longer side (the length). * Determine the number of intervals along the length (the row containing 12 columns of trees). $$\text{Intervals} = 12 - 1 = 11$$ * Calculate the distance spanned by these trees. $$\text{Tree Span} = 11 \text{ intervals} \times 2 \text{ metres/interval} = 22 \text{ metres}$$ * Account for the boundaries. The problem states 1 metre is left from *all* sides. This means 1 metre is added to the left end and 1 metre to the right end. $$\text{Total Length} = \text{Tree Span} + \text{Left Boundary} + \text{Right Boundary}$$ $$\text{Total Length} = 22 + 1 + 1 = 24 \text{ metres}$$ ### Exam Strategy & Shortcut Visualize the grid quickly. 12 trees mean 11 gaps. $11 \times 2 = 22$. Add 2 for the borders ($1+1$). Total is 24. For the width (if asked), 10 trees mean 9 gaps. $9 \times 2 = 18$. Add 2 for borders. Total is 20. Since "length" implies the maximum dimension, immediately choose 24. ### Common Pitfall Two common mistakes happen here: forgetting to subtract 1 from the number of trees to find the gaps, and forgetting that a 1-metre margin on "all sides" means adding 1 metre *twice* to any single dimensional length (once for each end). ### Final Answer Therefore, the correct answer is **24 m**.