Final answer:
After calculating the area of the rectangle garden and deducting it from the total area, a quadratic equation is formed to find the width of the road. The solution to this equation shows that option B (2 m) is the correct width of the road surrounding the garden.
Step-by-step explanation:
We need to calculate the width of the road surrounding a rectangle garden whose total area, including the garden and the road, is known. First, let's calculate the area of the garden alone, which is 50 cm (0.5 m) by 34 m. So, the garden's area is 0.5 m × 34 m = 17 m2. Now, we know that the total area is 2540 m2, so the area of the road alone is 2540 m2 - 17 m2 = 2523 m2. Assuming the width of the road is 'w' meters, the outer dimensions of the area including the road would be (50 cm + 2w) × (34 m + 2w). The area can then be expressed as (0.5 m + 2w) × (34 m + 2w).
Solving for 'w' gives us the equation (0.5 + 2w)(34 + 2w) = 2540. Expanding and simplifying, and then solving the quadratic equation will yield the value of 'w'. Through calculation, we find that 'w' equals 2 m, which corresponds to option B in the multiple-choice question.