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

Question

https://gmatclub.com/forum/download/file.php?id=36198 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 2017-07-11_1344.png

BrentGMATPrepNow · Accepted Answer

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: C

Cheers,
Brent

VivekLal · Answer

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

ScottTargetTestPrep · Answer

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

sonikavadhera · Answer

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

+1 kudos if u like the post.

brs1cob · Answer

answere is option C.

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

solve this equation n we get 5 as the answer.

arif24 · Answer

https://uploads.tapatalk-cdn.com/20170715/94bffb53f2a897e25e77b3f1e9813f14.jpg

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shreyashree · Answer

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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hellosanthosh2k2 · Answer

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)

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

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