The figure above shows a rectangular garden that is comprised of a

Question

https://gmatclub.com/forum/download/file.php?id=28380 The figure above shows a rectangular garden that is comprised of a central plot and a border surrounding the central plot; the border and the central plot have the same area. The garden has length 25 feet and width 20 feet. If the length and width of the central plot have the same ratio as the length and width of the garden, what is the length of the central plot, in feet? A. 25\sqrt{2} B. 20\sqrt{2} C. 20(1-\sqrt{2}) D. \frac{25\sqrt{2}}{2} E. (25/2)^2 Untitled.png

CounterSniper · Answer

let length and bredth of central plot be x and y therefore area =x*y as per the question 25*20-xy=xy 500=2xy > xy=250 now 25/20=x/y x/y=5/4 > 5x*4x=250 > x2 =250/20 > x =(25/2)^1/2 :?:

Skywalker18 · Answer

Let length of central plot = x
 width of central plot = y
 
 Since , the border and the central plot have the same area .
 x*y = 25*20 - x*y
 => 2*x*y = 500
 => x*y = 250 --- 1 
 
 Length and width of central plot have the same ratio as the length and width of the garden
 x/y = 25/20 = 5/4
 
 => y = (4/5)* x --- 2 
 
 Using equation 2 in equation 2 , we get
 (4/5) *x *x = 250
 => x^2 = 1250 / 4
 => x =  /2
 
 Answer D

chetan2u · Answer

Hi,
you are right upto x=(25/2)^1/2...
x=5/(2^1/2)..
we are looking for 5x=5*5/(2^1/2)=25/(2^1/2)
or 25(2^1/2)/2
ans D

CounterSniper · Answer

no wonder my answers dont match for half of the questions

kshitijkhurana3010 · Answer

The length and width of the central plot have the same ratio as the length and width of the garden,
Let the length be 5X and width be 4X for central Plot, so central plot area =  20X^{2} 
Area of central Plot = Area of border surrounding, So Area of border surrounding =  20X^{2} 
Area of central Plot + Area of border surrounding = Total Area 
 20X^{2}  +  20X^{2}  = 20 *25
 40X^{2}  = 500
X =  \frac{5}{\sqrt {2}} 
Length of central plot: 5X = 5* \frac{5}{\sqrt {2}}  =  \frac{25\sqrt {2}}{2}

Ans: D

DJ1986 · Answer

I solved it by looking at the answer choices and using logic/educated guessing/Luck.

Because the big rectangle's area is (500 - the little rectangle) = little rectangle. You can guess that the little one going to be about half the size. If it were a perfect square the lengths would be \sqrt{250}. 16^2=256 so we are looking for something that is a little bigger than 15ish.

Answers A, B and E make the length even longer than 25 so cross them out and C makes it 8 which is way too small leaving only D which is 17ish.

This could have been pure luck but I still got it right :-D

rohit8865 · Answer

Length of the central plot must be less than 25
if we analyse every option we see each one is greater than 25 exept (C)& (D)
but option (C) is rather a negative value which is immpossible
leaving option(D) as correct one
Ans D

generis · Answer

General equation 
Area of center = LW

Area of border = area of center = LW

Center + border = Total area (25*20)

2(LW) = 500 
 LW = 250

Use the ratio to eliminate W

The ratio of length to width of total area (garden) = ratio of length to width for center

\frac{L}{W} = \frac{25}{20} = \frac{5}{4}: 5W = 4L --> W = \frac{4}{5}L

Substitute and solve for length

LW = 250 
 W = \frac{4}{5}L

\frac{4}{5}L*L = 250

\frac{4}{5}L^2 = 250

L^2 =
250 * \frac{5}{4}

** L^2 =\frac{25*10*5}{4} = \frac{(25)*2*(5)*(5)}{4}

L =\frac{25\sqrt{2}}{2}

Answer D

**OR
 L^2 = (250 *\frac{5}{4}) =(\frac{1250}{4}) =(\frac{2*5*5*5*5}{4})

L =\frac{25\sqrt{2}}{2}

NinetyFour · Answer

My reasoning if it helps:

length : width = 25:20 = 5:4

width is equal =  \frac{4L}{5}

Area of border is equal to the area of the central plot.

Total area - central plot area = border area

25*20 - L*W = L*W

L*W = 250

We know from the ratio above that W =  \frac{4L}{5}

Hence L =  \frac{25*sqrt(2)}{2}

energetics · Answer

Checking answers approach: 
We are looking for the small rectangle length (l), which is somewhat bigger than half the big rectangle length (L=25) given the ratio L/W = 5/4. So our answer must be 13 (estimating) < l < 25. Using the fact that √2≈1.4 or 14/10=7/5, check the answers:

Can immediately eliminate C) and E) since C) 20*(1-1.4) gives a negative number and E) 12.5² is way bigger than 25

Check A) 25*7/5 = 35, too big
Check B) 25*7/5 = 25, still too big

Left with D) which is the same as A)/2 so 17.5, only answer that fits.

bumpbot · Answer

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