A vacant lot is being converted into a community garden. The garden and the walkway around its perimeter have an area of 238 ft2. Find the width of the walkway if the garden is 12 ft wide by 15 ft long. ft

Let us say that:

x = width of walkway

So the area is:

(12 + 2x) (15 + 2x) = 238

2x because we must add x on both sides of length and width

Expanding:

180 + 24x + 30x + 4x^2 = 238

4x^2 + 54x = 58

By completing the square:

x^2 + 13.5x + 45.5625 = 60.0625

(x + 6.75) ^2 = 60.0625

x + 6.75 = ±7.75

x = - 14.5, 1

Since dimension cannot be negative, therefore:

width = 1 ft