A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, then what is the area of the parking space in square feet?

### Concept & Formula A rectangle has two pairs of equal opposite sides (Length $L$ and Breadth $B$). If one side is unpainted, the remaining three sides consist of two sides of one dimension and one side of the other dimension. $$ \text{Area} = L \times B $$ ### Step-by-Step Solution * **Given:** Unpainted side = $9\text{ ft}$. Sum of three painted sides = $37\text{ ft}$. * **Logic:** The unpainted side must be one of the two dimensions (either length or breadth). Because opposite sides are equal, there must be a corresponding painted side that is also $9\text{ ft}$. * **Step 1:** Set up the equation for the painted sides. The three painted sides consist of one side of $9\text{ ft}$, and two sides of the unknown dimension (let's call it $x$). * **Step 2:** Solve for the unknown dimension. $2x + 9 = 37$ $2x = 37 - 9$ $2x = 28$ $x = 14\text{ ft}$ * **Step 3:** The dimensions of the parking space are $9\text{ ft}$ and $14\text{ ft}$. Calculate the area. $\text{Area} = 14 \times 9 = 126\text{ sq. ft.}$ ### Exam Strategy & Shortcut Recognize immediately that the sum of the remaining three sides must include the opposite side to the unpainted one. Subtract $9$ from $37$ to get $28$, which represents the sum of the two equal opposite sides. Halving $28$ gives the second dimension ($14$). Multiply $14$ by $9$ to get $126$. ### Common Pitfall A common error is assuming the unpainted side is necessarily the shorter or longer side, leading to confusion if one tries to strictly assign variables to "Length" and "Breadth" rather than just thinking in terms of opposite sides. ### Final Answer Therefore, the correct answer is **126**.