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Difficulty: 505-555 Level,    Geometry,                            
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Re: The figure shown above represents a modern painting that consists of f [#permalink]
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Bunuel wrote:

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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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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Bunuel wrote:

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]
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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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]
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]
This is a great question...One of the best questions in the official guide ..
Here => area => l^2+lw =4800 and l=3w => 12w^2 =4800 => w=20.
hence B
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Re: The figure shown above represents a modern painting that consists of f [#permalink]
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]
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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adkikani wrote:
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,
Arpit

adkikani
The other variable is (l+w)*l = 4800 which is total area given. OR (l+w)*3w = 4800
From there on you can solve for l and w both.

Also note that 3 horizontal areas form 1 square as 3w = l. So 1 vertical rectangle is \(\frac{1}{4}^{th}\) of the total area i.e. l*w = \(\frac{4800}{4}\) = 1200 as you have also done it.
Re: The figure shown above represents a modern painting that consists of f [#permalink]
Bunuel wrote:

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

E is the trap answer. For E the length is 120. So the area is 40*120=4800, which is the area of the whole painting, but we need width of each of the four rectangles, which is B (20).
Hope it helps...
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Re: The figure shown above represents a modern painting that consists of f [#permalink]
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Bunuel wrote:

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



The length \(l\) of the table is equal to the width \((w)\) of the small rectangle, \(l=3w\)

Width of the large table \(=3w+w=4w\)

Area of the large table \(=3w*4w=12w^2\)

Given, \(12w^2=4800\)

\(w^2=400\)

\(w=20\)

The answer is \(B\)
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Re: The figure shown above represents a modern painting that consists of f [#permalink]
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Bunuel wrote:

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


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Re: The figure shown above represents a modern painting that consists of f [#permalink]
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Video solution from Quant Reasoning:
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Re: The figure shown above represents a modern painting that consists of f [#permalink]
Correct option : B (20)
(LxW) x 4 = 4800 --- for all 4 rectangle
LxW = 1200 ------(1)
L=3W
3W^2 = 1200
W^2 = 400
W=(20,-20) ---(2) taking positive
L = 20x3 = 60
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Re: The figure shown above represents a modern painting that consists of f [#permalink]
Expert Reply
Bunuel wrote:

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



Attachment:
2015-10-19_0007.png


There are two ways to calculate the area of the entire painting:

Area of the entire painting = 4 * area of each rectangle = 4 * lw = 4800
This means lw = 1200

Area of the entire painting is also given by: \( l * (l + w) = l^2 + lw = 4800\)

Since lw = 1200,
\(l^2 = 4800 - 1200 = 3600\\
l = 60\\
w = 1200/l = 1200/60 = 20\)

Answer (B)
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Re: The figure shown above represents a modern painting that consists of f [#permalink]
Can be solved using common sense

60*80=4800

3W= 60

W= 20
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