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?

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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?

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Answer 1 · 2015-09-10T12:17:35

I found $3 ft$ $3"ft"$

Explanation:

You can take the total area $1248 {ft}^{2}$ $1248 "ft"^2$ and subtract the area of the garden which is $42 \cdot 20 = 840 {ft}^{2}$ $42*20=840 "ft"^2$ and get:
$1248 - 840 = 408 {ft}^{2}$ $1248-840=408 "ft"^2$
So:
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Answer 2 · 2015-09-10T12:22:33

The walkway is $3$ $3$ feet wide

Explanation:

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

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

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

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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

Explanation:

Explanation:

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