Question

A rectangular garden 42 by 20 feet is surrounded by a walk way of uniform width. If the total area of the garden and walkway is 1248 square feet, what is the the width of the walkway?

Answer 1

I found `3"ft"`

Explanation:

You can take the total area `1248 "ft"^2` and subtract the area of the garden which is `42*20=840 "ft"^2` and get:
`1248-840=408 "ft"^2`
So:

Answer 2

The walkway is `3` feet wide

Explanation:

Define
`color(white)("XXX")w`: width of walkway

Area of garden (including walkway)
`color(white)("XXX")(42+2w)xx(20+2w) = 1248`
With some basic algebra and arithmetic:
`rarrcolor(white)("XX")4w^2+124w+840 = 1248`
`rarrcolor(white)("XX")4w^2+124w-408 =0`
`rarrcolor(white)("XX")w^2+31w-102=0`
`rarrcolor(white)("XX")(w-3)(w+34) = 0`

and (since the width can't be a negative number)
`rarrcolor(white)("XX")w=3`