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?

Question

Accepted Answer

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 }3.5text{ meters}.})

Answer

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 }3.5text{ meters}.})

6. A rectangular lawn measuring $8 m$ by $4 m$ is surrounded by a flower bed of uniform width. The combined area of the lawn and the flower bed is $165 m^{2}$ . What is the width of the flower bed?

Answer

Popular Problems

6. A rectangular lawn measuring 8 m by 4 m is surrounded by a flower bed of uniform width. The combined area of the lawn and the flower bed is 165 m2. What is the width of the flower bed?

Answer

Popular Problems

6. A rectangular lawn measuring $8 m$ by $4 m$ is surrounded by a flower bed of uniform width. The combined area of the lawn and the flower bed is $165 m^{2}$ . What is the width of the flower bed?