6. A rectangular lawn measuring $8 \mathrm{~m}$ by $4 \mathrm{~m}$ is surrounded by a flower bed of uniform width. The combined area of the lawn and the flower bed is $165 \mathrm{~m}^{2}$. What is the width of the flower bed?
Answer
\(\boxed{\text{The width of the flower bed is }\frac{7}{2}\text{ meters or }3.5\text{ meters}.}\)
Step 1 ：Let the width of the flower bed be denoted as x. The dimensions of the lawn and flower bed combined would be \((8+2x)\) and \((4+2x)\).
Step 2 ：The area of the lawn is \(8 \times 4 = 32\) square meters.
Step 3 ：The area of the lawn and flower bed combined is 165 square meters. So, we can set up an equation: \((8+2x)(4+2x) = 165\).
Step 4 ：Solving this equation, we get two possible solutions for x: \(-\frac{19}{2}\) and \(\frac{7}{2}\).
Step 5 ：Since the width of the flower bed cannot be negative, we discard the \(-\frac{19}{2}\) solution.
Step 6 ：\(\boxed{\text{The width of the flower bed is }\frac{7}{2}\text{ meters or }3.5\text{ meters}.}\)
