A housing society has been allotted a square piece of land measuring 2550.25 sq. m. What is the side of the plot?

### Concept & Formula The area of a square is equal to the square of its side length. To find the side length from the area, calculate the square root. $$ \text{Area} = \text{side}^2 $$ ### Step-by-Step Solution - **Given**: Area of the square plot $= 2550.25$ sq. m. - Let the side of the plot be $a$. - According to the formula: $a^2 = 2550.25$. - To find $a$, take the square root of $2550.25$: $a = \sqrt{2550.25}$. - We know that $50^2 = 2500$ and $51^2 = 2601$. The value $2550.25$ lies between them. - Since the number ends in $.25$, its square root must end in $.5$. - Therefore, $a = 50.5$ m. ### Exam Strategy & Shortcut Use estimation to save time. $\sqrt{2500} = 50$. The target number is just slightly above $2500$ and ends in $5$ (ignoring the decimal for a moment), meaning the root must be $50.5$. You don't need to calculate the exact square root. ### Common Pitfall Attempting to use the long division method for the square root can consume too much time. Always check perfect squares nearby first. ### Final Answer Therefore, the correct answer is **50.5 m**.