Final answer:
To find the width of the flowerbed, subtract the area of the lawn from the combined area. Set up an equation using the dimensions of the flowerbed and solve for the width. The width of the flowerbed is approximately 1.983 meters.
Step-by-step explanation:
To find the width of the flowerbed, we need to subtract the area of the rectangular lawn from the combined area of the lawn and the flowerbed. The combined area is 165m^2 and the dimensions of the lawn are 8m by 4m. The area of the lawn is 8 * 4 = 32m^2. So, the area of the flowerbed is 165m^2 - 32m^2 = 133m^2.
Let the width of the flowerbed be 'x' meters. The dimensions of the flowerbed will be (8 + 2x) by (4 + 2x) meters. The area of the flowerbed can be expressed as (8 + 2x)(4 + 2x) = 133m^2.
Expanding this equation, we get 16x^2 + 32x + 32x + 64 = 133. Simplifying further, we get 16x^2 + 64x - 69 = 0. Solving this quadratic equation, we find x ~ 1.983m.
Therefore, the width of the flowerbed is approximately
1.983 meters