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?

2 Answers
Sep 10, 2015

Answer:

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:
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Sep 10, 2015

Answer:

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#