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

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



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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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

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

Answer: Option B

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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

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

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

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.
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how can you say that l=3w?

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

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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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)

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
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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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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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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

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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Can be solved using common sense

60*80=4800

3W= 60

W= 20