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Martin planted a rectangular garden with dimensions 20 feet by 30 feet

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Martin planted a rectangular garden with dimensions 20 feet by 30 feet [#permalink]

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Martin planted a rectangular garden with dimensions 20 feet by 30 feet and then surrounded the garden with a rectangular brick walkway of uniform width (represented by the shaded area in the drawing above). If the area of the walkway equals the area of the garden, what is the width of the walkway?

(A) 1 foot
(B) 3 feet
(C) 5 feet
(D) 8 feet
(E) 10 feet

[Reveal] Spoiler:
Attachment:
2017-07-11_1344.png
2017-07-11_1344.png [ 8.71 KiB | Viewed 1706 times ]
[Reveal] Spoiler: OA

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Re: Martin planted a rectangular garden with dimensions 20 feet by 30 feet [#permalink]

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New post 11 Jul 2017, 02:54
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Just pick the number 5. then outer length will become 20+2*5=30
and outer length will become 30+2*5=40
So the Area of bigger rectangle will be 30*40=1200
Area of inside Rectangle=30*20=600
So Are outer - Area inner will be 1200-600=600 which is true. So option C is correct
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Re: Martin planted a rectangular garden with dimensions 20 feet by 30 feet [#permalink]

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New post 11 Jul 2017, 05:56
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Bunuel wrote:
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Martin planted a rectangular garden with dimensions 20 feet by 30 feet and then surrounded the garden with a rectangular brick walkway of uniform width (represented by the shaded area in the drawing above). If the area of the walkway equals the area of the garden, what is the width of the walkway?

(A) 1 foot
(B) 3 feet
(C) 5 feet
(D) 8 feet
(E) 10 feet

[Reveal] Spoiler:
Attachment:
2017-07-11_1344.png


Here's an algebraic solution...

There are two areas to consider:
1) area of rectangular garden
2) area of walkway
We know the area of the garden = (20)(30) = 600 square feet.
Since the area of the walkway EQUALS the area of the garden, the area of the walkway also equals 600 square feet.

So, the area of the OUTER rectangle (which includes both the garden and the walkway) = 600 + 600 = 1200

What are the dimensions of the OUTER rectangle?
They are 20 + 2x by 30 + 2x
We can write: (20 + 2x)(30 + 2x) = 1200
Expand and simplify: 600 + 100x + 4x² = 1200
Rearrange to get: 4x² + 100x - 600 = 0
Divide both sides by 4 to get: x² + 25x - 150 = 0
Factor: (x + 30)(x - 5) = 0

So, EITHER x = -30 OR x = 5
Since the width of the walkway (x) cannot be negative, we can conclude that x = 5

Answer:
[Reveal] Spoiler:
C


Cheers,
Brent
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Re: Martin planted a rectangular garden with dimensions 20 feet by 30 feet [#permalink]

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New post 12 Jul 2017, 17:15
Bunuel wrote:
Image
Martin planted a rectangular garden with dimensions 20 feet by 30 feet and then surrounded the garden with a rectangular brick walkway of uniform width (represented by the shaded area in the drawing above). If the area of the walkway equals the area of the garden, what is the width of the walkway?

(A) 1 foot
(B) 3 feet
(C) 5 feet
(D) 8 feet
(E) 10 feet


We can let the length of the walkway plus the garden = 30 + 2x, and the width of the walkway plus the garden = 20 + 2x, and create the following equation:

(30 + 2x)(20 + 2x) - 600 = 600

600 + 100x + 4x^2 - 600 = 600

4x^2 + 100x - 600 = 0

x^2 + 25x - 150 = 0

(x + 30)(x - 5) = 0

x = -30 or x = 5

Since x cannot be negative, x = 5.

Answer: C
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Re: Martin planted a rectangular garden with dimensions 20 feet by 30 feet [#permalink]

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New post 14 Jul 2017, 01:14
Total area = area of garden + area of walkway

(30 + 2x)(20 + 2x) = 600 + 600

600 + 60x + 40x + 4x^2 - 1200 = 0

x^2 + 25x + 150 = 0

x = -30 or +5

as width can't be negative; answer is + 5 -- Option C

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Re: Martin planted a rectangular garden with dimensions 20 feet by 30 feet [#permalink]

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New post 15 Jul 2017, 10:18
answere is option C.

600 = 2(30*d) + (20*d)2 + 4d^2

solve this equation n we get 5 as the answer.
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Re: Martin planted a rectangular garden with dimensions 20 feet by 30 feet [#permalink]

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New post 15 Jul 2017, 10:36
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Re: Martin planted a rectangular garden with dimensions 20 feet by 30 feet [#permalink]

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New post 15 Jul 2017, 10:52
Option C would be the right answer..

I would do back substitution and solve. That's how I picked 5 to start with and solved.

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Re: Martin planted a rectangular garden with dimensions 20 feet by 30 feet [#permalink]

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New post 18 Mar 2018, 22:28
Since area of garden = area of walkway,
area of garden/total area = 1/2

total area = 1200
(30 + 2x)(20 + 2x) = 1200, back solving works better, we can pick x = 5 => Answer (C)
Re: Martin planted a rectangular garden with dimensions 20 feet by 30 feet   [#permalink] 18 Mar 2018, 22:28
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