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The figure shown above represents a modern painting that consists of f

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The figure shown above represents a modern painting that consists of f  [#permalink]

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New post 18 Oct 2015, 12:10
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Question Stats:

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The figure shown above represents a modern painting that consists of four differently colored rectangles, each of which has length ℓ and width w. If the area of the painting is 4,800 square inches, what is the width, in inches, of each of the four rectangles?

(A) 15
(B) 20
(C) 25
(D) 30
(E) 40

Kudos for a correct solution.

Attachment:
2015-10-19_0007.png
2015-10-19_0007.png [ 5.85 KiB | Viewed 11210 times ]

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Re: The figure shown above represents a modern painting that consists of f  [#permalink]

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New post 03 May 2016, 05:49
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Bunuel wrote:
Image
The figure shown above represents a modern painting that consists of four differently colored rectangles, each of which has length ℓ and width w. If the area of the painting is 4,800 square inches, what is the width, in inches, of each of the four rectangles?

(A) 15
(B) 20
(C) 25
(D) 30
(E) 40

Kudos for a correct solution.

Attachment:
2015-10-19_0007.png


Let’s begin by sketching the given diagram. We can also add in the appropriate dimensions to each side.

Image

From the diagram we can create an equation:

l = w + w + w

l= 3w

We also know that the area is 4,800 square inches. Using the dimensions from our diagram and the formula for the area of a rectangle, we can say:

l(w + l) = 4,800

Since l = 3w, we can substitute 3w for l in the area equation l(w + l) = 4,800. Thus, we have:

3w(w + 3w) = 4,800

3w(4w) = 4,800

12w^2 = 4,800

w^2 = 400

w = ±20

Because we are dealing with a measurement, we disregard w = -20 as a solution. Thus, the width of each rectangle is 20 inches.

Answer: B
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Re: The figure shown above represents a modern painting that consists of f  [#permalink]

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New post 18 Oct 2015, 12:33
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Bunuel wrote:
Image
The figure shown above represents a modern painting that consists of four differently colored rectangles, each of which has length ℓ and width w. If the area of the painting is 4,800 square inches, what is the width, in inches, of each of the four rectangles?

(A) 15
(B) 20
(C) 25
(D) 30
(E) 40

Kudos for a correct solution.

Attachment:
2015-10-19_0007.png


As shown in Figure, l = 3w

The area of each small rectangle = l*w = 4,800/4 = 12*100

=> 3w*w = 12*100

=> w = 20

Ans: B
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Re: The figure shown above represents a modern painting that consists of f  [#permalink]

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New post 18 Oct 2015, 21:26
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Bunuel wrote:
Image
The figure shown above represents a modern painting that consists of four differently colored rectangles, each of which has length ℓ and width w. If the area of the painting is 4,800 square inches, what is the width, in inches, of each of the four rectangles?

(A) 15
(B) 20
(C) 25
(D) 30
(E) 40

Kudos for a correct solution.

Attachment:
2015-10-19_0007.png



we have l = 3w

so area of rectangle = l * (l + w) = 4800
=> 3w ( 3w + w) = 4800
=> 12 w^2 = 4800
=> w^2 = 400
=> w = 20 (taking +ve value)

Answer choice B
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Re: The figure shown above represents a modern painting that consists of f  [#permalink]

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New post 28 Mar 2016, 12:45
from the figure we can see that l = 3w
4 rectangles have a combined area 4lw = 4800
therefore lw=1200
substituting l = 3w in above equation
3w^2=1200
w^2 = 400
taking positive square roots
w= 20

answer - B
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Re: The figure shown above represents a modern painting that consists of f  [#permalink]

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New post 29 Mar 2016, 01:13
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Bunuel wrote:
Image
The figure shown above represents a modern painting that consists of four differently colored rectangles, each of which has length ℓ and width w. If the area of the painting is 4,800 square inches, what is the width, in inches, of each of the four rectangles?

(A) 15
(B) 20
(C) 25
(D) 30
(E) 40

Kudos for a correct solution.

Attachment:
2015-10-19_0007.png


Observation 1: ℓ = 3w
Observation 2: ℓ*(ℓ+w) = 4800

i.e. 3w*(3w+w) = 4800

i.e. 12w^2 = 4800

i.e. w^2 = 400

i.e. w = 20 and ℓ = 60

Answer: Option B
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Re: The figure shown above represents a modern painting that consists of f  [#permalink]

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New post 02 Apr 2016, 06:43
how can you say that l=3w?
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Re: The figure shown above represents a modern painting that consists of f  [#permalink]

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New post 02 Apr 2016, 11:57
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andreroma wrote:
how can you say that l=3w?

As you can see from the figure 3 small rectangles stacked in a linear fashion (horizontal ones where length appears to be bigger)
3 small widths = 3w (addition of three widths of the 3 above mentioned rectangles)
As can be figured out from the larger rectangle the addition of 3 smaller widths correspond to length of the remaining smaller rectangle
Therefore l=3w can be deduced

Hope the explaination helps
+1 kudos if you like it
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Re: The figure shown above represents a modern painting that consists of f  [#permalink]

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New post 02 Apr 2016, 12:48
equation 1: (l+w)(3w)=4800
equation 2: 4lw=4800➡l=1200/w
substituting for l in equation 1,
(1200/w+w)(3w)=4800
w=20
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Re: The figure shown above represents a modern painting that consists of f  [#permalink]

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New post 03 Apr 2016, 14:56
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Re: The figure shown above represents a modern painting that consists of f  [#permalink]

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New post 02 May 2016, 13:37
Good stuff, gotta recognize a simple pattern here to solve in 30 seconds

the image shows you that l=3w

given, A of all = 4800. 4 pieces of equal length means then that lw = 1200

l=3w
lw=1200
3w(w)=1200
3w^2 = 1200
w^2 = 400
w=20 (cannot be -20, we are in feasibility mode here)
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Re: The figure shown above represents a modern painting that consists of f  [#permalink]

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New post 19 Aug 2017, 08:55
Bunuel Engr2012 shashankism

Can you help to understand flaw in below approach:
it is clear that the figure consists of one vertical rectangle and three horizontal rectangles.

Step 1: for all three horizontal rectangles area = 3 (l * w)
Step 2: for one vertical rectangles area = l*w

so total area of figure = 4 l* w (summation of above steps) which is given as 4800 as per Q stem.

We need two variables or need to express l / w in terms of another. Here is where I got stuck and could not proceed.

WR,
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Re: The figure shown above represents a modern painting that consists of f  [#permalink]

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