The area of a grassy plot is 480 sq. m. If each side had been 5 m longer, the area would have been increased by 245 sq. m. Find the length of the fence to surround it. (M.B.A. 2007)

### Concept & Perimeter Calculation The "length of the fence to surround it" refers to the perimeter of the rectangular plot. Let the original length and breadth be $l$ and $b$. We can set up two equations based on the given areas to solve for $(l + b)$. Formulas: $$Area = l \times b$$ $$Perimeter = 2(l + b)$$ ### Step-by-Step Solution * **Given:** Original Area = $lb = 480$. * If each side is increased by 5m, the new dimensions are $(l + 5)$ and $(b + 5)$. * The new area is $480 + 245 = 725$ sq. m. * Equation: $(l + 5)(b + 5) = 725$. * Expand the equation: $lb + 5l + 5b + 25 = 725$. * Substitute $lb = 480$: $480 + 5(l + b) + 25 = 725$. * Simplify: $505 + 5(l + b) = 725$. * $5(l + b) = 725 - 505 = 220$. * Divide by 5: $l + b = 44$. * The length of the fence is the perimeter: $2(l + b) = 2 \times 44 = 88$ m. ### Exam Strategy & Shortcut We directly isolated $(l + b)$ without solving for the individual values of $l$ and $b$. This is the fastest approach when only the perimeter is required. ### Common Pitfall A common mistake is spending too much time trying to form a quadratic equation to find the exact values of length and breadth, which is completely unnecessary to find the perimeter. ### Final Answer Therefore, the correct answer is **88 m**.