The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 7803 sq. metres, What is the breadth of the rectangular plot? (Bank P.O. 2009)

### Concept & Algebraic Substitution When one dimension is given as a multiple of another, express both dimensions in terms of a single variable to create an equation based on the area formula. $$ \text{Area} = \text{Length} \times \text{Breadth} $$ ### Step-by-Step Solution * **Given:** Length ($L$) is thrice its breadth ($B$), so $L = 3B$. Area = $7803\text{ sq. m}$. * **Step 1:** Substitute the expressions into the area formula. $3B \times B = 7803$ $3B^2 = 7803$ * **Step 2:** Solve for $B^2$. $B^2 = \frac{7803}{3}$ $B^2 = 2601$ * **Step 3:** Find $B$ by taking the square root. $B = \sqrt{2601}$ $B = 51\text{ m}$ ### Exam Strategy & Shortcut To quickly find the square root of $2601$, look at the ending digit ($1$) and the first two digits ($26$). The nearest perfect square below $26$ is $25$ ($5^2$), so the root is in the 50s. Since it ends in $1$, the root must end in $1$ or $9$. $50^2 = 2500$, which is very close to $2601$, so it must be $51$. This allows you to skip manual square root extraction. ### Common Pitfall A common error is forgetting to square the variable $B$ when multiplying $3B \times B$, mistakenly writing $3B = 7803$ which would yield $B = 2601$. Always maintain proper algebraic rules during substitution. ### Final Answer Therefore, the correct answer is **51 m**.