A rectangular garden measuring 10 m by 16 m is to be surrounded by a concrete walk of uniform width. If the area of the walk is 120 m², find the width of the walk.

To find the width of the walk surrounding a 10 m by 16 m garden with the walk's area being 120 m², we set up an equation based on the total area that includes the garden and the walk. By solving the equation, we discover that the width of the walk is 2 m.

Explanation:

The question involves finding the width of the walk that surrounds a rectangular garden with dimensions of 10 m by 16 m. Given that the area of the walk is 120 m², we are looking for a uniform width, let's call it w, that when applied to all sides of the garden, creates a larger rectangle whose area is the sum of the garden's area and the walk's area.

First, calculate the area of the garden: 10 m imes 16 m = 160 m². The combined area of the garden and the walk is 160 m² + 120 m² = 280 m². The outer dimensions of the walk plus the garden become (10 + 2w) m by (16 + 2w) m. Setting up the equation for the new area gives us:

(10 + 2w)(16 + 2w) = 280.

Expanding and solving this quadratic equation will provide the value for w, the width of the walk. This equation results in w being equal to 2 m after simplification and solving for w.