GMAT CLUB OLYMPICS: A square shown above is divided into 5 rectangles,

Question

https://gmatclub.com/forum/download/file.php?id=62906 A square shown above is divided into 5 rectangles, each having the same area. If the upper left rectangle has a width of 5 units, then what is the area of the square? A. 100 B. 169 C. 225 D. 400 E. 625 Untitled.png

HarshaBujji · Accepted Answer

Please ref. then attachment for better understanding.

Let us assume the side of the square is s,
So total area of the square is  s^2

As we know all the rectangles inscribed in the square are of the same area  A , 
=>  s^2  = 5A, 
So area of each rectangle is  s^2 /5;

So Ar  = Ar  =  s^2 /5;

We know AD=5; So AB= Ar /AD =  s^2 /25;
Similarly, We know CG=s; So BC= Ar /CG = s/5;

AC = AB + BC =  s^2 /25 + s/5;
We also know AC=s

Hence s=  s^2 /25 + s/5;
So s=20 or 0;
As s=0 is not possible; s=20;

Hence area of square  s^2  = 400;

IMO D

Bunuel · Answer

Official Solution:

https://gmatclub.com/tests-beta/resources/import/img/M37-32.png 
 
A square shown above is divided into 5 rectangles, each having the same area. If the upper left rectangle has a width of 5 units, then what is the area of the square?

A.  100 
B.  169 
C.  225 
D.  400 
E.  625

https://gmatclub.com/tests-beta/resources/import/img/M37-32-2.png 
 
Say the length of the purple rectangle is  x . Then the area of all 5 rectangles will be  5x .
 
Say the length of the red rectangle is  y . Then the combined area of red, yellow, and green rectangles will be  xy , as well as  5x+5x+5x=15x . 
 
So,  xy=15x . This gives:  y=15 .
 
The side of the square is  5+y=20  and the area is  20^2=400 .

Answer: D

avijitsrivastava · Answer

Assume the square to be of side L and the light blue rectangle to be of horizontal length X. Then, as per the directions of the question,

LX = (L^2)/5 (Area of blue rectangle is one-fifth of the total area of the square)

Hence,

X = L/5

Now comparing the purple rectangle with the blue one

5*(L-X) = LX
=> 4L = (L^2)/5
=> L = 20

Therefore, area of the square will be:

L^2 = 400

Answer: (D) 400

Kinshook · Answer

https://gmatclub.com/forum/download/file.php?id=62906 Given: A square shown above is divided into 5 rectangles, each having the same area. Asked: If the upper left rectangle has a width of 5 units, then what is the area of the square? Screenshot 2021-08-16 at 8.57.45 PM.png Since the area of all rectangles is same. 5(x + y) = ty = 2tx = (2t+5)z y = 2x 15x = 2tx t = 7.5 15x = 20z 3x = 4z Since all rectangles combined form a square 2t+5 = x+ y+z 20 = x + 2x + 3x/4 = 15x/4 x = 80/15 = 16/3 y = 32/3 z = 4 Area of the square = (2t+5)^2 = 20^2 = 400 IMO D

soudipsengupta · Answer

I would go backward from the answer choices:

Option A is 100 as area of square:

Area Square (S): 100
Side of Square : 10
Long Side of Red (R): 5
Area of Purple(P): 100/5=20
Long Side of P: 20/5=4
Area of Red + Yellow + Green= R * P = 5*4=20 ....(1)
But since Red + Yellow + Green must be equal area as 3 * Area of Purple (i.e. 3*20=60) ... (2)
From 1 and 2 A option is not correct.

On similar terms and since 100 led to a small combined area of the 3 rectangles next chose a bigger option like. Like D is 400 and more likely to the answer.

Area Square (S): 400
Side of Square : 20
Long Side of Red (R): 15
Area of Purple(P): 400/5=80
Long Side of P: 80/5=16
Area of Red + Yellow + Green= R * P = 15*16=240 ....(3)
But since Red + Yellow + Green must be equal area as 3 * Area of Purple (i.e. 3*80=240) ... (4)

From 3 and 4 we see these matches hence D is the right answer.

bish4l · Answer

The area of the square is given as l^2.
Let the area of the rectangle be considered as 5x such that say, x is the length of the rectangle.
Also, since the area of the rectangles is same. So, all the areas would be 5x.
Now let us consider only red, yellow and green rectangles. The sum of their areas would be 15x.
Also, the area can be written as x*y(where y is the vertical length of the three rectangles(r, y & g combined).)
So,
15x=x*y
thus the vertical length would be 15
Hence, the side of square would be (15+5) and 
area of square would be 20^2=400

chetan2u · Answer

Let the area of the rectangles be to A to E as shown.  =>  A=B=C=D=E

Given that  B+C+D=3*A

A=5*b
B+C+D=x*b
=> x*b=3*5*b
x=15

So, each side of the square = 5+15

Area = 20*20=400

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GMAT CLUB OLYMPICS: A square shown above is divided into 5 rectangles,

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