High School

The length and width of a rectangular garden are 150 m and 120 m. A footpath of regular width is added to the boundary of the garden, and the total area of the garden becomes 2800 m\(^2\) more than its original area. Find the width of the footpath.

Answer :

Final answer:

To find the width of the footpath, we set up an equation using the original length and width of the garden and solve for x.

Explanation:

Let's denote the width of the footpath as 'x'.

The new length of the garden would be (150 + 2x) and the new width would be (120 + 2x).

The original area of the garden is given by 150 * 120 = 18000 square meters.

The new area of the garden is given by (150 + 2x) * (120 + 2x).

The problem states that the new area is 2800 square meters more than the original area, so we can set up the equation:

(150 + 2x) * (120 + 2x) = 18000 + 2800.

Simplifying and solving this equation will give us the width of the footpath.

x=5

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