The breadth of a rectangular field is $\frac{3}{4}$ of its length and its area is 300 sq. metres. What will be the area (in sq. metres) of the garden of breadth 1.5 metres developed around the field?

### Concept & Algebraic Geometry Leverage area and fractional ratio properties to uncover base dimensions before executing border expansions. $$ Area = L \times \left(\frac{3}{4}L\right) $$ ### Step-by-Step Solution * Initial field proportions are equated to quickly solve for base base length and breadth variables. * Boundary expansions rigorously define the new bounding frame. * Uncomplicated area computation outputs 114 directly. ### Exam Strategy & Shortcut Solving $0.75L^2 = 300$ immediately gives $L=20, B=15$. The garden area formula is $2W(L + B + 2W)$. Using $W=1.5$, this becomes $3(20 + 15 + 3) = 3(38) = 114$. ### Common Pitfall Mistaking the descriptive word "around" to mean constructing the garden inside the boundary, which triggers an erroneous subtraction of the border width instead of an addition. ### Final Answer Therefore, the correct answer is **114**.